Jadczyk, Arkadiusz On the bundle of Clifford algebras over the space of quadratic forms. (English) Zbl 1518.15025 Adv. Appl. Clifford Algebr. 33, No. 2, Paper No. 15, 32 p. (2023). Reviewer: Eckhard Hitzer (Tokyo) MSC: 15A66 15A63 32G08 15A75 PDFBibTeX XMLCite \textit{A. Jadczyk}, Adv. Appl. Clifford Algebr. 33, No. 2, Paper No. 15, 32 p. (2023; Zbl 1518.15025) Full Text: DOI arXiv
Breuils, Stephane; Nozick, Vincent; Sugimoto, Akihiro Computational aspects of geometric algebra products of two homogeneous multivectors. (English) Zbl 1505.15020 Adv. Appl. Clifford Algebr. 33, No. 1, Paper No. 4, 39 p. (2023). MSC: 15A66 68Q17 PDFBibTeX XMLCite \textit{S. Breuils} et al., Adv. Appl. Clifford Algebr. 33, No. 1, Paper No. 4, 39 p. (2023; Zbl 1505.15020) Full Text: DOI arXiv
Akar, Mutlu A generalization of Euler’s formula in Clifford algebras. (English) Zbl 07780637 Math. Methods Appl. Sci. 45, No. 7, 4069-4080 (2022). MSC: 15A66 11E88 15A75 15A03 PDFBibTeX XMLCite \textit{M. Akar}, Math. Methods Appl. Sci. 45, No. 7, 4069--4080 (2022; Zbl 07780637) Full Text: DOI
Dinh, D. C. Monogenic functions with values in generalized Clifford algebras. (English) Zbl 1502.30140 Ukr. Math. J. 73, No. 11, 1712-1722 (2022) and Ukr. Mat. Zh. 73, No. 11, 1483-1491 (2021). MSC: 30G35 15A66 PDFBibTeX XMLCite \textit{D. C. Dinh}, Ukr. Math. J. 73, No. 11, 1712--1722 (2022; Zbl 1502.30140) Full Text: DOI
Wieser, Eric; Song, Utensil Formalizing geometric algebra in Lean. (English) Zbl 1494.68307 Adv. Appl. Clifford Algebr. 32, No. 3, Paper No. 28, 26 p. (2022). Reviewer: Eckhard Hitzer (Tokyo) MSC: 68V20 11E88 15A66 15A67 PDFBibTeX XMLCite \textit{E. Wieser} and \textit{U. Song}, Adv. Appl. Clifford Algebr. 32, No. 3, Paper No. 28, 26 p. (2022; Zbl 1494.68307) Full Text: DOI arXiv Backlinks: MO
Breuils, Stephane; Tachibana, Kanta; Hitzer, Eckhard New applications of Clifford’s geometric algebra. (English) Zbl 1490.15036 Adv. Appl. Clifford Algebr. 32, No. 2, Paper No. 17, 39 p. (2022). Reviewer: Morteza Shahpari (Adelaide) MSC: 15A67 15A66 68T01 68U05 11E88 70E60 94A12 PDFBibTeX XMLCite \textit{S. Breuils} et al., Adv. Appl. Clifford Algebr. 32, No. 2, Paper No. 17, 39 p. (2022; Zbl 1490.15036) Full Text: DOI
Abłamowicz, Rafał On the structure of ternary Clifford algebras and their irreducible representations. (English) Zbl 1483.15015 Adv. Appl. Clifford Algebr. 32, No. 1, Paper No. 11, 39 p. (2022). Reviewer: Adam Chapman (Tel Hai) MSC: 15A66 16W50 20C05 20C15 20D15 PDFBibTeX XMLCite \textit{R. Abłamowicz}, Adv. Appl. Clifford Algebr. 32, No. 1, Paper No. 11, 39 p. (2022; Zbl 1483.15015) Full Text: DOI
Byrtus, Roman; Derevianko, Anna; Vašík, Petr; Hildenbrand, Dietmar; Steinmetz, Christian On specific conic intersections in GAC and symbolic calculations in GAALOPWeb. (English) Zbl 1478.15033 Adv. Appl. Clifford Algebr. 32, No. 1, Paper No. 2, 21 p. (2022); correction ibid. 32, No. 1, Paper No. 8, 2 p. (2022). MSC: 15A67 51N25 PDFBibTeX XMLCite \textit{R. Byrtus} et al., Adv. Appl. Clifford Algebr. 32, No. 1, Paper No. 2, 21 p. (2022; Zbl 1478.15033) Full Text: DOI
Shirokov, D. S. On computing the determinant, other characteristic polynomial coefficients, and inverse in Clifford algebras of arbitrary dimension. (English) Zbl 1476.65061 Comput. Appl. Math. 40, No. 5, Paper No. 173, 29 p. (2021). MSC: 65F40 68W30 15A66 PDFBibTeX XMLCite \textit{D. S. Shirokov}, Comput. Appl. Math. 40, No. 5, Paper No. 173, 29 p. (2021; Zbl 1476.65061) Full Text: DOI arXiv
Arcodía, Marcos R. A. Complexifying the spacetime algebra by means of an extra timelike dimension: pin, spin and algebraic spinors. (English) Zbl 1461.15028 Adv. Appl. Clifford Algebr. 31, No. 2, Paper No. 17, 28 p. (2021). Reviewer: Adam Chapman (Tel Hai) MSC: 15A66 15A67 83C60 53C27 PDFBibTeX XMLCite \textit{M. R. A. Arcodía}, Adv. Appl. Clifford Algebr. 31, No. 2, Paper No. 17, 28 p. (2021; Zbl 1461.15028) Full Text: DOI arXiv
Hadfield, Hugo; Achawal, Sushant; Lasenby, Joan; Lasenby, Anthony; Young, Benjamin Exploring novel surface representations via an experimental ray-tracer in CGA. (English) Zbl 1509.65017 Adv. Appl. Clifford Algebr. 31, No. 2, Paper No. 16, 33 p. (2021). MSC: 65D18 15A67 51N20 53A31 PDFBibTeX XMLCite \textit{H. Hadfield} et al., Adv. Appl. Clifford Algebr. 31, No. 2, Paper No. 16, 33 p. (2021; Zbl 1509.65017) Full Text: DOI
Abłamowicz, Rafał The Moore-Penrose inverse and singular value decomposition of split quaternions. (English) Zbl 1444.15004 Adv. Appl. Clifford Algebr. 30, No. 3, Paper No. 33, 20 p. (2020). Reviewer: Hans-Peter Schröcker (Innsbruck) MSC: 15A09 15A18 15A66 15A23 PDFBibTeX XMLCite \textit{R. Abłamowicz}, Adv. Appl. Clifford Algebr. 30, No. 3, Paper No. 33, 20 p. (2020; Zbl 1444.15004) Full Text: DOI
Sousa, Eduardo Vera; Fernandes, Leandro A. F. TbGAL: a tensor-based library for geometric algebra. (English) Zbl 1433.15004 Adv. Appl. Clifford Algebr. 30, No. 2, Paper No. 27, 33 p. (2020). MSC: 15-04 15A66 68W30 PDFBibTeX XMLCite \textit{E. V. Sousa} and \textit{L. A. F. Fernandes}, Adv. Appl. Clifford Algebr. 30, No. 2, Paper No. 27, 33 p. (2020; Zbl 1433.15004) Full Text: DOI
Bayro-Corrochano, Eduardo Geometric algebra applications Vol. I. Computer vision, graphics and neurocomputing. (English) Zbl 1475.68004 Cham: Springer (ISBN 978-3-319-74828-3/hbk; 978-3-030-09085-2/pbk; 978-3-319-74830-6/ebook). xxxiii, 742 p. (2019). MSC: 68-02 15A67 68Txx 68U05 68U10 PDFBibTeX XMLCite \textit{E. Bayro-Corrochano}, Geometric algebra applications Vol. I. Computer vision, graphics and neurocomputing. Cham: Springer (2019; Zbl 1475.68004) Full Text: DOI
Li, Li-Ming; Shi, Zhi-Ping; Guan, Yong; Zhang, Qian-Ying; Li, Yong-Dong Formalization of geometric algebra in HOL Light. (English) Zbl 1468.68329 J. Autom. Reasoning 63, No. 3, 787-808 (2019). MSC: 68V20 15A66 PDFBibTeX XMLCite \textit{L.-M. Li} et al., J. Autom. Reasoning 63, No. 3, 787--808 (2019; Zbl 1468.68329) Full Text: DOI
Cheng, Tao; Li, Huilan; Yang, Yuping A new view of generalized Clifford algebras. (English) Zbl 1415.15025 Adv. Appl. Clifford Algebr. 29, No. 3, Paper No. 42, 11 p. (2019). Reviewer: Adam Chapman (Upper Galilee) MSC: 15A66 18D10 16S35 PDFBibTeX XMLCite \textit{T. Cheng} et al., Adv. Appl. Clifford Algebr. 29, No. 3, Paper No. 42, 11 p. (2019; Zbl 1415.15025) Full Text: DOI
Hitzer, Eckhard; Sangwine, Stephen J. Construction of multivector inverse for Clifford algebras over \(2m+1\)-dimensional vector spaces from multivector inverse for Clifford algebras over \(2m\)-dimensional vector spaces. (English) Zbl 1458.15042 Adv. Appl. Clifford Algebr. 29, No. 2, Paper No. 29, 22 p. (2019). MSC: 15A66 11E88 15A15 15A09 PDFBibTeX XMLCite \textit{E. Hitzer} and \textit{S. J. Sangwine}, Adv. Appl. Clifford Algebr. 29, No. 2, Paper No. 29, 22 p. (2019; Zbl 1458.15042) Full Text: DOI
Soto-Francés, Víctor-Manuel; Sarabia-Escrivá, Emilio-José; Pinazo-Ojer, José-Manuel Consistently oriented dart-based 3D modelling by means of geometric algebra and combinatorial maps. (English) Zbl 1452.68248 Adv. Appl. Clifford Algebr. 29, No. 1, Paper No. 19, 53 p. (2019). MSC: 68U05 15A66 51M20 PDFBibTeX XMLCite \textit{V.-M. Soto-Francés} et al., Adv. Appl. Clifford Algebr. 29, No. 1, Paper No. 19, 53 p. (2019; Zbl 1452.68248) Full Text: DOI
Trindade, Marco A. S.; Pinto, Eric; Floquet, Sergio Clifford algebras, multipartite systems and gauge theory gravity. (English) Zbl 1408.83010 Adv. Appl. Clifford Algebr. 29, No. 1, Paper No. 1, 17 p. (2019). MSC: 83C05 15A66 16T05 81P40 81P45 83C57 70S15 PDFBibTeX XMLCite \textit{M. A. S. Trindade} et al., Adv. Appl. Clifford Algebr. 29, No. 1, Paper No. 1, 17 p. (2019; Zbl 1408.83010) Full Text: DOI arXiv
Hrdina, Jaroslav; Návrat, Aleš; Vašík, Petr Notes on planar inverse kinematics based on geometric algebra. (English) Zbl 1393.70010 Adv. Appl. Clifford Algebr. 28, No. 3, Paper No. 71, 14 p. (2018). MSC: 70B15 15A66 68U10 PDFBibTeX XMLCite \textit{J. Hrdina} et al., Adv. Appl. Clifford Algebr. 28, No. 3, Paper No. 71, 14 p. (2018; Zbl 1393.70010) Full Text: DOI
Hrdina, Jaroslav; Návrat, Aleš; Vašík, Petr Geometric algebra for conics. (English) Zbl 1398.51045 Adv. Appl. Clifford Algebr. 28, No. 3, Paper No. 66, 21 p. (2018). Reviewer: Victor V. Pambuccian (Yerevan) MSC: 51N25 15A66 PDFBibTeX XMLCite \textit{J. Hrdina} et al., Adv. Appl. Clifford Algebr. 28, No. 3, Paper No. 66, 21 p. (2018; Zbl 1398.51045) Full Text: DOI
Abłamowicz, Rafał Spinor modules of Clifford algebras in classes \(N_{2k-1}\) and \(\Omega _{2k-1}\) are determined by irreducible nonlinear characters of corresponding Salingaros vee groups. (English) Zbl 1395.15017 Adv. Appl. Clifford Algebr. 28, No. 2, Paper No. 51, 19 p. (2018). Reviewer: Adam Chapman (Upper Galilee) MSC: 15A66 20C05 20C15 PDFBibTeX XMLCite \textit{R. Abłamowicz}, Adv. Appl. Clifford Algebr. 28, No. 2, Paper No. 51, 19 p. (2018; Zbl 1395.15017) Full Text: DOI
Abłamowicz, Rafał; Varahagiri, Manisha; Walley, Anne Marie A classification of Clifford algebras as images of group algebras of Salingaros vee groups. (English) Zbl 1394.15016 Adv. Appl. Clifford Algebr. 28, No. 2, Paper No. 38, 34 p. (2018). MSC: 15A66 16W50 20C05 20C40 20D15 68W30 PDFBibTeX XMLCite \textit{R. Abłamowicz} et al., Adv. Appl. Clifford Algebr. 28, No. 2, Paper No. 38, 34 p. (2018; Zbl 1394.15016) Full Text: DOI
Eid, Ahmad Hosny An extended implementation framework for geometric algebra operations on systems of coordinate frames of arbitrary signature. (English) Zbl 1390.68776 Adv. Appl. Clifford Algebr. 28, No. 1, Paper No. 16, 32 p. (2018). MSC: 68W30 15A66 PDFBibTeX XMLCite \textit{A. H. Eid}, Adv. Appl. Clifford Algebr. 28, No. 1, Paper No. 16, 32 p. (2018; Zbl 1390.68776) Full Text: DOI
Hitzer, Eckhard; Sangwine, Stephen Multivector and multivector matrix inverses in real Clifford algebras. (English) Zbl 1426.15035 Appl. Math. Comput. 311, 375-389 (2017). MSC: 15A66 11E88 15A09 PDFBibTeX XMLCite \textit{E. Hitzer} and \textit{S. Sangwine}, Appl. Math. Comput. 311, 375--389 (2017; Zbl 1426.15035) Full Text: DOI Link
Hrdina, Jaroslav; Návrat, Aleš Binocular computer vision based on conformal geometric algebra. (English) Zbl 1425.68420 Adv. Appl. Clifford Algebr. 27, No. 3, 1945-1959 (2017). MSC: 68T45 15A66 68U05 PDFBibTeX XMLCite \textit{J. Hrdina} and \textit{A. Návrat}, Adv. Appl. Clifford Algebr. 27, No. 3, 1945--1959 (2017; Zbl 1425.68420) Full Text: DOI
Ulrych, S. Conformal numbers. (English) Zbl 1369.30066 Adv. Appl. Clifford Algebr. 27, No. 2, 1895-1906 (2017). MSC: 30G35 15A66 PDFBibTeX XMLCite \textit{S. Ulrych}, Adv. Appl. Clifford Algebr. 27, No. 2, 1895--1906 (2017; Zbl 1369.30066) Full Text: DOI arXiv
Korepanov, I. G. Free fermions on a piecewise linear four-manifold. I: Exotic chain complex. (English) Zbl 1391.15081 Adv. Appl. Clifford Algebr. 27, No. 2, 1411-1430 (2017). Reviewer: Martin Plešinger (Liberec) MSC: 15A66 15A63 81T99 PDFBibTeX XMLCite \textit{I. G. Korepanov}, Adv. Appl. Clifford Algebr. 27, No. 2, 1411--1430 (2017; Zbl 1391.15081) Full Text: DOI arXiv
Prodanov, D.; Toth, V. T. Sparse representations of Clifford and tensor algebras in maxima. (English) Zbl 1367.15040 Adv. Appl. Clifford Algebr. 27, No. 1, 661-683 (2017). MSC: 15A66 15A69 78A25 78M25 11E88 94B27 53A45 PDFBibTeX XMLCite \textit{D. Prodanov} and \textit{V. T. Toth}, Adv. Appl. Clifford Algebr. 27, No. 1, 661--683 (2017; Zbl 1367.15040) Full Text: DOI arXiv
Franchini, Silvia; Gentile, Antonio; Sorbello, Filippo; Vassallo, Giorgio; Vitabile, Salvatore Embedded coprocessors for native execution of geometric algebra operations. (English) Zbl 1367.15034 Adv. Appl. Clifford Algebr. 27, No. 1, 559-580 (2017). MSC: 15A66 68U05 68W30 PDFBibTeX XMLCite \textit{S. Franchini} et al., Adv. Appl. Clifford Algebr. 27, No. 1, 559--580 (2017; Zbl 1367.15034) Full Text: DOI
Sangwine, Stephen J.; Hitzer, Eckhard Clifford multivector toolbox (for MATLAB). (English) Zbl 1407.68566 Adv. Appl. Clifford Algebr. 27, No. 1, 539-558 (2017). MSC: 68W30 11E88 15A66 PDFBibTeX XMLCite \textit{S. J. Sangwine} and \textit{E. Hitzer}, Adv. Appl. Clifford Algebr. 27, No. 1, 539--558 (2017; Zbl 1407.68566) Full Text: DOI Link
Helmstetter, Jacques Conformal groups and Vahlen matrices. (English) Zbl 1381.11027 Adv. Appl. Clifford Algebr. 27, No. 1, 33-44 (2017). Reviewer: Adam Chapman (Upper Galilee) MSC: 11E57 15A66 PDFBibTeX XMLCite \textit{J. Helmstetter}, Adv. Appl. Clifford Algebr. 27, No. 1, 33--44 (2017; Zbl 1381.11027) Full Text: DOI
Zhang, Feng; Jiang, Xiaomin; Zhang, Xiaoyi; Wang, Yingzhi; Du, Zhenhong; Liu, Renyi Unified spatial intersection algorithms based on conformal geometric algebra. (English) Zbl 1400.68252 Math. Probl. Eng. 2016, Article ID 7412373, 10 p. (2016). MSC: 68U05 15A66 PDFBibTeX XMLCite \textit{F. Zhang} et al., Math. Probl. Eng. 2016, Article ID 7412373, 10 p. (2016; Zbl 1400.68252) Full Text: DOI
Trayling, Greg Metric and involution scores of Clifford algebras. (English) Zbl 1377.15013 Adv. Appl. Clifford Algebr. 26, No. 4, 1331-1340 (2016). Reviewer: Jaydeb Sarkar (Bangalore) MSC: 15A66 PDFBibTeX XMLCite \textit{G. Trayling}, Adv. Appl. Clifford Algebr. 26, No. 4, 1331--1340 (2016; Zbl 1377.15013) Full Text: DOI
Fuchs, Laurent; Théry, Laurent Implementing geometric algebra products with binary trees. (English) Zbl 1311.68147 Adv. Appl. Clifford Algebr. 24, No. 2, 589-611 (2014). MSC: 68T15 11E88 15A66 PDFBibTeX XMLCite \textit{L. Fuchs} and \textit{L. Théry}, Adv. Appl. Clifford Algebr. 24, No. 2, 589--611 (2014; Zbl 1311.68147) Full Text: DOI
Abłamowicz, Rafał; Fauser, Bertfried Using periodicity theorems for computations in higher dimensional Clifford algebras. (English) Zbl 1298.65073 Adv. Appl. Clifford Algebr. 24, No. 2, 569-587 (2014). MSC: 65F30 15A66 PDFBibTeX XMLCite \textit{R. Abłamowicz} and \textit{B. Fauser}, Adv. Appl. Clifford Algebr. 24, No. 2, 569--587 (2014; Zbl 1298.65073) Full Text: DOI arXiv
Abłamowicz, Rafał; Fauser, Bertfried On parallelizing the Clifford algebra product for CLIFFORD. (English) Zbl 1298.65072 Adv. Appl. Clifford Algebr. 24, No. 2, 553-567 (2014). MSC: 65F30 15A66 65Y15 PDFBibTeX XMLCite \textit{R. Abłamowicz} and \textit{B. Fauser}, Adv. Appl. Clifford Algebr. 24, No. 2, 553--567 (2014; Zbl 1298.65072) Full Text: DOI arXiv
Zamora-Esquivel, Julio \(G_{6,3}\) geometric algebra; description and implementation. (English) Zbl 1298.15033 Adv. Appl. Clifford Algebr. 24, No. 2, 493-514 (2014). MSC: 15A66 PDFBibTeX XMLCite \textit{J. Zamora-Esquivel}, Adv. Appl. Clifford Algebr. 24, No. 2, 493--514 (2014; Zbl 1298.15033) Full Text: DOI
Hitzer, Eckhard Two-sided Clifford Fourier transform with two square roots of \(-1\) in \(Cl(p,q)\). (English) Zbl 1301.42017 Adv. Appl. Clifford Algebr. 24, No. 2, 313-332 (2014). MSC: 42B10 15A66 94A12 PDFBibTeX XMLCite \textit{E. Hitzer}, Adv. Appl. Clifford Algebr. 24, No. 2, 313--332 (2014; Zbl 1301.42017) Full Text: DOI arXiv
Hitzer, Eckhard; Helmstetter, Jacques; Abłamowicz, Rafał Square roots of \(-1\) in real Clifford algebras. (English) Zbl 1273.15025 Hitzer, Eckhard (ed.) et al., Quaternion and Clifford Fourier transforms and wavelets. Papers from a session of the 9th international conference on Clifford algebras and their applications, ICCA9, Weimar, Germany, July 15–20, 2011. New York, NY: Birkhäuser/Springer (ISBN 978-3-0348-0602-2/hbk; 978-3-0348-0603-9/ebook). Trends in Mathematics, 123-153 (2013). MSC: 15A66 11E88 42A38 30G35 PDFBibTeX XMLCite \textit{E. Hitzer} et al., in: Quaternion and Clifford Fourier transforms and wavelets. Papers from a session of the 9th international conference on Clifford algebras and their applications, ICCA9, Weimar, Germany, July 15--20, 2011. New York, NY: Birkhäuser/Springer. 123--153 (2013; Zbl 1273.15025) Full Text: DOI arXiv
Hitzer, Eckhard; Nitta, Tohru; Kuroe, Yasuaki Applications of Clifford’s geometric algebra. (English) Zbl 1269.15022 Adv. Appl. Clifford Algebr. 23, No. 2, 377-404 (2013). MSC: 15A66 15-02 PDFBibTeX XMLCite \textit{E. Hitzer} et al., Adv. Appl. Clifford Algebr. 23, No. 2, 377--404 (2013; Zbl 1269.15022) Full Text: DOI arXiv
Helmstetter, Jacques A survey of Lipschitz monoids. (English) Zbl 1254.15027 Adv. Appl. Clifford Algebr. 22, No. 3, 665-688 (2012). MSC: 15A66 16S80 PDFBibTeX XMLCite \textit{J. Helmstetter}, Adv. Appl. Clifford Algebr. 22, No. 3, 665--688 (2012; Zbl 1254.15027) Full Text: DOI
Abłamowicz, Rafał; Fauser, Bertfried On the transposition anti-involution in real Clifford algebras. III: The automorphism group of the transposition scalar product on spinor spaces. (English) Zbl 1388.15021 Linear Multilinear Algebra 60, No. 6, 621-644 (2012). MSC: 15A66 16S35 20C05 68W30 PDFBibTeX XMLCite \textit{R. Abłamowicz} and \textit{B. Fauser}, Linear Multilinear Algebra 60, No. 6, 621--644 (2012; Zbl 1388.15021) Full Text: DOI arXiv
Franchini, Silvia; Gentile, Antonio; Sorbello, Filippo; Vassallo, Giorgio; Vitabile, Salvatore Fixed-size quadruples for a new, hardware-oriented representation of the 4D Clifford algebra. (English) Zbl 1251.15028 Adv. Appl. Clifford Algebr. 21, No. 2, 315-340 (2011). MSC: 15A66 65D18 68U05 68W30 PDFBibTeX XMLCite \textit{S. Franchini} et al., Adv. Appl. Clifford Algebr. 21, No. 2, 315--340 (2011; Zbl 1251.15028) Full Text: DOI
Abłamowicz, Rafał; Fauser, Bertfried On the transposition anti-involution in real Clifford algebras. II: Stabilizer groups of primitive idempotents. (English) Zbl 1393.15030 Linear Multilinear Algebra 59, No. 12, 1359-1381 (2011). MSC: 15A66 11E88 68W30 PDFBibTeX XMLCite \textit{R. Abłamowicz} and \textit{B. Fauser}, Linear Multilinear Algebra 59, No. 12, 1359--1381 (2011; Zbl 1393.15030) Full Text: DOI arXiv
Abłamowicz, Rafał; Fauser, Bertfried On the transposition anti-involution in real Clifford algebras. I: The transposition map. (English) Zbl 1393.15029 Linear Multilinear Algebra 59, No. 12, 1331-1358 (2011). MSC: 15A66 11E88 68W30 PDFBibTeX XMLCite \textit{R. Abłamowicz} and \textit{B. Fauser}, Linear Multilinear Algebra 59, No. 12, 1331--1358 (2011; Zbl 1393.15029) Full Text: DOI arXiv
Scharnhorst, K.; van Holten, J.-W. Nonlinear Bogolyubov-Valatin transformations: two modes. (English) Zbl 1252.81092 Ann. Phys. 326, No. 11, 2868-2933 (2011). MSC: 81T05 81R05 81T60 15A66 15B33 81R15 81R25 PDFBibTeX XMLCite \textit{K. Scharnhorst} and \textit{J. W. van Holten}, Ann. Phys. 326, No. 11, 2868--2933 (2011; Zbl 1252.81092) Full Text: DOI arXiv
Hitzer, Eckhard; Abłamowicz, Rafał Geometric roots of \(-1\) in Clifford algebras \(C \ell_{p,q}\) with \(p + q \leq 4\). (English) Zbl 1216.15019 Adv. Appl. Clifford Algebr. 21, No. 1, 121-144 (2011). MSC: 15A66 15B33 11E88 42A38 30G35 PDFBibTeX XMLCite \textit{E. Hitzer} and \textit{R. Abłamowicz}, Adv. Appl. Clifford Algebr. 21, No. 1, 121--144 (2011; Zbl 1216.15019) Full Text: DOI arXiv
Helmstetter, Jacques Lipschitzian subspaces in Clifford algebras. (English) Zbl 1217.15033 J. Algebra 328, No. 1, 461-483 (2011). Reviewer: Grozio Stanilov (Sofia) MSC: 15A66 14N20 15A75 20M32 PDFBibTeX XMLCite \textit{J. Helmstetter}, J. Algebra 328, No. 1, 461--483 (2011; Zbl 1217.15033) Full Text: DOI
Abłamowicz, Rafał Computations with Clifford and Grassmann algebras. (English) Zbl 1182.65068 Adv. Appl. Clifford Algebr. 19, No. 3-4, 499-545 (2009). MSC: 65F30 15A66 15A75 65Y15 PDFBibTeX XMLCite \textit{R. Abłamowicz}, Adv. Appl. Clifford Algebr. 19, No. 3--4, 499--545 (2009; Zbl 1182.65068) Full Text: DOI
Sobczyk, Garret Geometric matrix algebra. (English) Zbl 1149.15024 Linear Algebra Appl. 429, No. 5-6, 1163-1173 (2008). Reviewer: Piwen Yang (Sichuan) MSC: 15A66 15B33 51F25 PDFBibTeX XMLCite \textit{G. Sobczyk}, Linear Algebra Appl. 429, No. 5--6, 1163--1173 (2008; Zbl 1149.15024) Full Text: DOI
da Rocha, R.; Vaz, J. Isotopic liftings of Clifford algebras and applications in elementary particle mass matrices. (English) Zbl 1133.81062 Int. J. Theor. Phys. 46, No. 10, 2464-2487 (2007). MSC: 81V35 15A66 PDFBibTeX XMLCite \textit{R. da Rocha} and \textit{J. Vaz}, Int. J. Theor. Phys. 46, No. 10, 2464--2487 (2007; Zbl 1133.81062) Full Text: DOI arXiv
Fauser, Bertfried Products, coproducts, and singular value decomposition. (English) Zbl 1119.18007 Int. J. Theor. Phys. 45, No. 9, 1731-1755 (2006). MSC: 18D10 15A18 PDFBibTeX XMLCite \textit{B. Fauser}, Int. J. Theor. Phys. 45, No. 9, 1731--1755 (2006; Zbl 1119.18007) Full Text: DOI arXiv
Abłamowicz, Rafał; Fauser, Bertfried Clifford and Graßmann Hopf algebras via the BIGEBRA package for Maple. (English) Zbl 1196.16042 Comput. Phys. Commun. 170, No. 2, 115-130 (2005). MSC: 16Z05 16T05 15A75 81R05 81R50 16-04 PDFBibTeX XMLCite \textit{R. Abłamowicz} and \textit{B. Fauser}, Comput. Phys. Commun. 170, No. 2, 115--130 (2005; Zbl 1196.16042) Full Text: DOI arXiv
Ablamowicz, Rafal; Fauser, Bertfried Mathematics of Clifford – a Maple package for Clifford and Graßmann algebras. (English) Zbl 1099.65520 Adv. Appl. Clifford Algebr. 15, No. 2, 157-181 (2005). MSC: 65F30 15A66 65Y15 PDFBibTeX XMLCite \textit{R. Ablamowicz} and \textit{B. Fauser}, Adv. Appl. Clifford Algebr. 15, No. 2, 157--181 (2005; Zbl 1099.65520) Full Text: DOI arXiv
Abłamowicz, Rafał (ed.); Sobczyk, Garret (ed.) [Baylis, William E.; Branson, Thomas; Lounesto, Pertti; Porteous, Ian; Ryan, John; Selig, J. M.; Ablamowicz, R.; Sobczyk, G.] Lectures on Clifford (geometric) algebras and applications. (English) Zbl 1058.15033 Boston, MA: Birkhäuser. (ISBN 0-8176-3257-3/pbk). xvii, 221 p. (2004). Reviewer: Waldyr A. Rodrigues (Campinas) MSC: 15A66 11E88 15-06 30G35 83C60 15A75 15-02 PDFBibTeX XML
Schmeikal, Bernd Minimal spin gauge theory. Clifford algebra and quantum chromodynamics. (English) Zbl 1038.81066 Adv. Appl. Clifford Algebr. 11, No. 1, 63-80 (2001). MSC: 81V05 15A66 81R25 81T13 PDFBibTeX XMLCite \textit{B. Schmeikal}, Adv. Appl. Clifford Algebr. 11, No. 1, 63--80 (2001; Zbl 1038.81066) Full Text: DOI
Pappas, Richard C. The geometric algebra \({\mathcal C}\ell_3\) as a model for a projective plane. (English) Zbl 1037.15022 Adv. Appl. Clifford Algebr. 11, No. 1, 1-13 (2001). MSC: 15A66 51E15 PDFBibTeX XMLCite \textit{R. C. Pappas}, Adv. Appl. Clifford Algebr. 11, No. 1, 1--13 (2001; Zbl 1037.15022) Full Text: DOI
Fauser, Bertfried Clifford geometric parameterization of inequivalent vacua. (English) Zbl 0990.15017 Math. Methods Appl. Sci. 24, No. 12, 885-912 (2001). Reviewer: Michael Shapiro (Mexico) MSC: 15A66 81S05 81R25 15A90 PDFBibTeX XMLCite \textit{B. Fauser}, Math. Methods Appl. Sci. 24, No. 12, 885--912 (2001; Zbl 0990.15017) Full Text: DOI arXiv
Fauser, Bertfried; Abłamowicz, Rafał On the decomposition of Clifford algebras of arbitrary bilinear form. (English) Zbl 0955.15018 Abłamowicz, Rafał (ed.) et al., Clifford algebras and their applications in mathematical physics. Proceedings of the 5th conference, Ixtapa-Zihuatanejo, Mexico, June 27-July 4, 1999. Volume 1: Algebra and physics. Boston, MA: Birkhäuser. Prog. Phys. 18, 341-366 (2000). MSC: 15A66 15A90 15A69 17B37 81R25 81R50 PDFBibTeX XMLCite \textit{B. Fauser} and \textit{R. Abłamowicz}, Prog. Phys. 18, 341--366 (2000; Zbl 0955.15018) Full Text: arXiv
Abłamowicz, Rafał; Fauser, Bertfried Hecke algebra representations in ideals generated by \(q\)-Young Clifford idempotents. (English) Zbl 0956.15014 Abłamowicz, Rafał (ed.) et al., Clifford algebras and their applications in mathematical physics. Proceedings of the 5th conference, Ixtapa-Zihuatanejo, Mexico, June 27-July 4, 1999. Volume 1: Algebra and physics. Boston, MA: Birkhäuser. Prog. Phys. 18, 245-268 (2000). MSC: 15A66 17B37 20C30 81R25 PDFBibTeX XMLCite \textit{R. Abłamowicz} and \textit{B. Fauser}, Prog. Phys. 18, 245--268 (2000; Zbl 0956.15014) Full Text: arXiv
Bergdolt, G. Isomorphism groups in Clifford algebras. (English) Zbl 0949.15038 Adv. Appl. Clifford Algebr. 9, No. 1, 95-101 (1999). Reviewer: Wolfgang Sproessig (Freiberg) MSC: 15A66 68W30 PDFBibTeX XMLCite \textit{G. Bergdolt}, Adv. Appl. Clifford Algebr. 9, No. 1, 95--101 (1999; Zbl 0949.15038) Full Text: DOI
Abłamowicz, Rafał Matrix exponential via Clifford algebras. (English) Zbl 0951.15024 J. Nonlinear Math. Phys. 5, No. 3, 294-313 (1998). Reviewer: B.Fauser (Tübingen) MSC: 15A66 15A18 15A54 15A21 81R25 15A90 PDFBibTeX XMLCite \textit{R. Abłamowicz}, J. Nonlinear Math. Phys. 5, No. 3, 294--313 (1998; Zbl 0951.15024) Full Text: DOI arXiv
Dray, Tevian; Manogue, Corinne A. Finding octonionic eigenvectors using Mathematica. (English) Zbl 1002.65046 Comput. Phys. Commun. 115, No. 2-3, 536-547 (1998). MSC: 65F15 15B33 15A18 PDFBibTeX XMLCite \textit{T. Dray} and \textit{C. A. Manogue}, Comput. Phys. Commun. 115, No. 2--3, 536--547 (1998; Zbl 1002.65046) Full Text: DOI arXiv
Abłamowicz, Rafał Spinor representations of Clifford algebras: A symbolic approach. (English) Zbl 1001.15020 Comput. Phys. Commun. 115, No. 2-3, 510-535 (1998). MSC: 15A66 15A75 65F30 65Y15 68W30 PDFBibTeX XMLCite \textit{R. Abłamowicz}, Comput. Phys. Commun. 115, No. 2--3, 510--535 (1998; Zbl 1001.15020) Full Text: DOI
Aragón, G.; Aragón, J. L.; Rodríguez, M. A. Clifford algebras and geometric algebra. (English) Zbl 0906.15020 Adv. Appl. Clifford Algebr. 7, No. 2, 91-102 (1997). Reviewer: Waldyr A.Rodrigues (Campinas) MSC: 15A66 PDFBibTeX XMLCite \textit{G. Aragón} et al., Adv. Appl. Clifford Algebr. 7, No. 2, 91--102 (1997; Zbl 0906.15020) Full Text: DOI
Abłamowicz, Rafał Clifford algebra computations with Maple. (English) Zbl 0861.15043 Baylis, William E. (ed.), Clifford (geometric) algebras with applications to physics, mathematics, and engineering. Proceedings of the 1995 summer school on theoretical physics, held in Banff, Canada, July 30–August 12, 1995. Boston, MA: Birkhäuser. 463-501 (1996). MSC: 15A66 68W30 15A63 65F30 PDFBibTeX XMLCite \textit{R. Abłamowicz}, in: Clifford (geometric) algebras with applications to physics, mathematics, and engineering. Proceedings of the 1995 summer school on theoretical physics, held in Banff, Canada, July 30--August 12, 1995. Boston, MA: Birkhäuser. 463--501 (1996; Zbl 0861.15043)
Abłamowicz, Rafał; Lounesto, Pertti On Clifford algebras of a bilinear form with an antisymmetric part. (English) Zbl 0856.15028 Abłamowicz, Rafał (ed.) et al., Clifford algebras with numeric and symbolic computations. Boston, MA: Birkhäuser. 167-188 (1996). Reviewer: B.Fauser (Tübingen) MSC: 15A66 15-04 15A75 68W30 PDFBibTeX XMLCite \textit{R. Abłamowicz} and \textit{P. Lounesto}, in: Clifford algebras with numeric and symbolic computations. Boston, MA: Birkhäuser. 167--188 (1996; Zbl 0856.15028)
Abłamowicz, Rafał (ed.); Lounesto, Pertti (ed.); Parra, Josep M. (ed.) Clifford algebras with numeric and symbolic computations. (English) Zbl 0846.00005 Boston, MA: Birkhäuser. xvii, 322 p. (1996). MSC: 00B15 15-06 53-06 PDFBibTeX XMLCite \textit{R. Abłamowicz} (ed.) et al., Clifford algebras with numeric and symbolic computations. Boston, MA: Birkhäuser (1996; Zbl 0846.00005)