Filimoshina, Ekaterina; Shirokov, Dmitry On some Lie groups in degenerate Clifford geometric algebras. (English) Zbl 1527.15020 Adv. Appl. Clifford Algebr. 33, No. 4, Paper No. 44, 29 p. (2023). Reviewer: Adam Chapman (Tel Hai) MSC: 15A66 15A67 22E47 22E66 PDFBibTeX XMLCite \textit{E. Filimoshina} and \textit{D. Shirokov}, Adv. Appl. Clifford Algebr. 33, No. 4, Paper No. 44, 29 p. (2023; Zbl 1527.15020) Full Text: DOI arXiv
Helmstetter, Jacques Various characteristic properties of Lipschitzian elements in Clifford algebras. (English) Zbl 1528.15022 Adv. Appl. Clifford Algebr. 33, No. 4, Paper No. 43, 29 p. (2023). Reviewer: Eckhard Hitzer (Tōkyō) MSC: 15A66 81R25 51F25 PDFBibTeX XMLCite \textit{J. Helmstetter}, Adv. Appl. Clifford Algebr. 33, No. 4, Paper No. 43, 29 p. (2023; Zbl 1528.15022) Full Text: DOI
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
Helmstetter, Jacques Equations satisfied by the coordinates of Lipschitzian elements in Clifford algebras. (English) Zbl 1505.15021 Adv. Appl. Clifford Algebr. 33, No. 1, Paper No. 7, 37 p. (2023). MSC: 15A66 15A63 20M32 PDFBibTeX XMLCite \textit{J. Helmstetter}, Adv. Appl. Clifford Algebr. 33, No. 1, Paper No. 7, 37 p. (2023; Zbl 1505.15021) Full Text: DOI
Abdulkhaev, Kamron; Shirokov, Dmitry Basis-free formulas for characteristic polynomial coefficients in geometric algebras. (English) Zbl 1505.15019 Adv. Appl. Clifford Algebr. 32, No. 5, Paper No. 57, 27 p. (2022). Reviewer: Sirkka-Liisa Eriksson (Helsinki) MSC: 15A66 11E88 15A15 68W30 PDFBibTeX XMLCite \textit{K. Abdulkhaev} and \textit{D. Shirokov}, Adv. Appl. Clifford Algebr. 32, No. 5, Paper No. 57, 27 p. (2022; Zbl 1505.15019) Full Text: DOI arXiv
Anglès, Pierre Siegel-Satake cross and associated Clifford algebras. (English) Zbl 1506.11059 Adv. Appl. Clifford Algebr. 32, No. 5, Paper No. 53, 28 p. (2022). Reviewer: Meinhard Peters (Münster) MSC: 11E88 15A63 15A66 53D05 11F46 PDFBibTeX XMLCite \textit{P. Anglès}, Adv. Appl. Clifford Algebr. 32, No. 5, Paper No. 53, 28 p. (2022; Zbl 1506.11059) Full Text: DOI
Oba, Roger M. Biquaternion extensions of analytic functions. (English) Zbl 1508.30094 Adv. Appl. Clifford Algebr. 32, No. 4, Paper No. 47, 26 p. (2022). MSC: 30G35 15A66 PDFBibTeX XMLCite \textit{R. M. Oba}, Adv. Appl. Clifford Algebr. 32, No. 4, Paper No. 47, 26 p. (2022; Zbl 1508.30094) Full Text: DOI
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
Shirokov, Dmitry Basis-free solution to Sylvester equation in Clifford algebra of arbitrary dimension. (English) Zbl 1476.15029 Adv. Appl. Clifford Algebr. 31, No. 5, Paper No. 70, 19 p. (2021). MSC: 15A24 15A66 15A67 15A09 PDFBibTeX XMLCite \textit{D. Shirokov}, Adv. Appl. Clifford Algebr. 31, No. 5, Paper No. 70, 19 p. (2021; Zbl 1476.15029) Full Text: DOI arXiv
Girard, Patrick R.; Clarysse, Patrick; Pujol, Romaric; Goutte, Robert; Delachartre, Philippe Hyperquaternion conformal groups. (English) Zbl 1477.15021 Adv. Appl. Clifford Algebr. 31, No. 3, Paper No. 56, 14 p. (2021). Reviewer: Sirkka-Liisa Eriksson (Helsinki) MSC: 15A66 11E88 15A67 15A69 PDFBibTeX XMLCite \textit{P. R. Girard} et al., Adv. Appl. Clifford Algebr. 31, No. 3, Paper No. 56, 14 p. (2021; Zbl 1477.15021) Full Text: DOI HAL
Mahmoudi, M. G.; Sidhwa, H. H. On constant-trace representations of degenerate Clifford algebras. (English) Zbl 1472.15031 Adv. Appl. Clifford Algebr. 31, No. 3, Paper No. 52, 17 p. (2021). MSC: 15A66 16R20 16S36 PDFBibTeX XMLCite \textit{M. G. Mahmoudi} and \textit{H. H. Sidhwa}, Adv. Appl. Clifford Algebr. 31, No. 3, Paper No. 52, 17 p. (2021; Zbl 1472.15031) Full Text: DOI
Shirokov, Dmitry On inner automorphisms preserving fixed subspaces of Clifford algebras. (English) Zbl 1466.15025 Adv. Appl. Clifford Algebr. 31, No. 3, Paper No. 30, 23 p. (2021). Reviewer: Adam Chapman (Tel Hai) MSC: 15A66 11E88 PDFBibTeX XMLCite \textit{D. Shirokov}, Adv. Appl. Clifford Algebr. 31, No. 3, Paper No. 30, 23 p. (2021; Zbl 1466.15025) Full Text: DOI arXiv
Helmstetter, Jacques Pseudo-inverses without matrices. (English) Zbl 1460.16040 Adv. Appl. Clifford Algebr. 31, No. 1, Paper No. 4, 31 p. (2021). Reviewer: Peter Danchev (Sofia) MSC: 16U90 15A66 PDFBibTeX XMLCite \textit{J. Helmstetter}, Adv. Appl. Clifford Algebr. 31, No. 1, Paper No. 4, 31 p. (2021; Zbl 1460.16040) Full Text: DOI
El Haoui, Youssef; Hitzer, Eckhard; Fahlaoui, Said Heisenberg’s and Hardy’s uncertainty principles for special relativistic space-time Fourier transformation. (English) Zbl 1454.15017 Adv. Appl. Clifford Algebr. 30, No. 5, Paper No. 69, 27 p. (2020). Reviewer: Nikhil Khanna (New Delhi) MSC: 15A67 83A05 42A38 42B05 30H10 PDFBibTeX XMLCite \textit{Y. El Haoui} et al., Adv. Appl. Clifford Algebr. 30, No. 5, Paper No. 69, 27 p. (2020; Zbl 1454.15017) Full Text: DOI
Helmstetter, Jacques Kanzaki’s generalized quadratic spaces and graded Salingaros groups. (English) Zbl 1457.15022 Adv. Appl. Clifford Algebr. 30, No. 4, Paper No. 60, 38 p. (2020). MSC: 15A63 11E88 15A66 PDFBibTeX XMLCite \textit{J. Helmstetter}, Adv. Appl. Clifford Algebr. 30, No. 4, Paper No. 60, 38 p. (2020; Zbl 1457.15022) 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
Vaz, Jayme jun. On paravectors and their associated algebras. (English) Zbl 1411.15014 Adv. Appl. Clifford Algebr. 29, No. 2, Paper No. 32, 18 p. (2019). Reviewer: Adam Chapman (Upper Galilee) MSC: 15A66 15A63 15A75 81R05 PDFBibTeX XMLCite \textit{J. Vaz jun.}, Adv. Appl. Clifford Algebr. 29, No. 2, Paper No. 32, 18 p. (2019; Zbl 1411.15014) Full Text: DOI
Helmstetter, Jacques Characteristic polynomials in Clifford algebras and in more general algebras. (English) Zbl 1428.15008 Adv. Appl. Clifford Algebr. 29, No. 2, Paper No. 30, 23 p. (2019). Reviewer: Eckhard Hitzer (Tokyo) MSC: 15A15 16S50 15A66 15A30 PDFBibTeX XMLCite \textit{J. Helmstetter}, Adv. Appl. Clifford Algebr. 29, No. 2, Paper No. 30, 23 p. (2019; Zbl 1428.15008) Full Text: DOI
Acus, A.; Dargys, A. The inverse of a multivector: beyond the threshold \(p+q=5\). (English) Zbl 1394.15004 Adv. Appl. Clifford Algebr. 28, No. 3, Paper No. 65, 20 p. (2018). MSC: 15A18 15A66 PDFBibTeX XMLCite \textit{A. Acus} and \textit{A. Dargys}, Adv. Appl. Clifford Algebr. 28, No. 3, Paper No. 65, 20 p. (2018; Zbl 1394.15004) Full Text: DOI arXiv
Anglès, Pierre A few comments on Ado’s theorem and non-linear Lie groups. (English) Zbl 1425.22006 Adv. Appl. Clifford Algebr. 28, No. 3, Paper No. 55, 15 p. (2018). Reviewer: Raed Raffoul (Sydney) MSC: 22E15 11E88 15A66 16S30 16W25 16W10 PDFBibTeX XMLCite \textit{P. Anglès}, Adv. Appl. Clifford Algebr. 28, No. 3, Paper No. 55, 15 p. (2018; Zbl 1425.22006) Full Text: DOI
Helmstetter, Jacques About a theorem of Hyman Bass and some other topics. (English) Zbl 1407.15030 Adv. Appl. Clifford Algebr. 28, No. 2, Paper No. 47, 19 p. (2018). Reviewer: Drahoslava Janovská (Praha) MSC: 15A66 22E45 PDFBibTeX XMLCite \textit{J. Helmstetter}, Adv. Appl. Clifford Algebr. 28, No. 2, Paper No. 47, 19 p. (2018; Zbl 1407.15030) 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
Tingelstad, Lars; Egeland, Olav Motor parameterization. (English) Zbl 1397.51014 Adv. Appl. Clifford Algebr. 28, No. 2, Paper No. 34, 15 p. (2018). MSC: 51N99 15A66 70E15 51N20 PDFBibTeX XMLCite \textit{L. Tingelstad} and \textit{O. Egeland}, Adv. Appl. Clifford Algebr. 28, No. 2, Paper No. 34, 15 p. (2018; Zbl 1397.51014) Full Text: DOI
Helmstetter, Jacques Bilinear forms derived from Lipschitzian elements in Clifford algebras. (English) Zbl 1392.15033 Adv. Appl. Clifford Algebr. 28, No. 1, Paper No. 25, 37 p. (2018). Reviewer: Adam Chapman (Upper Galilee) MSC: 15A66 15A78 PDFBibTeX XMLCite \textit{J. Helmstetter}, Adv. Appl. Clifford Algebr. 28, No. 1, Paper No. 25, 37 p. (2018; Zbl 1392.15033) Full Text: DOI
Hitzer, Eckhard General steerable two-sided Clifford Fourier transform, convolution and mustard convolution. (English) Zbl 1382.42007 Adv. Appl. Clifford Algebr. 27, No. 3, 2215-2234 (2017). MSC: 42B10 44A35 30G35 43A32 PDFBibTeX XMLCite \textit{E. Hitzer}, Adv. Appl. Clifford Algebr. 27, No. 3, 2215--2234 (2017; Zbl 1382.42007) Full Text: DOI
Hitzer, Eckhard Quaternionic Wiener-Khinchine theorems and spectral representation of convolution with steerable two-sided quaternion Fourier transform. (English) Zbl 1368.42010 Adv. Appl. Clifford Algebr. 27, No. 2, 1313-1328 (2017). MSC: 42B10 94A12 PDFBibTeX XMLCite \textit{E. Hitzer}, Adv. Appl. Clifford Algebr. 27, No. 2, 1313--1328 (2017; Zbl 1368.42010) Full Text: DOI
Helmstetter, Jacques Universal algebras \(\mathcal U(V,Q)\) for quadratic mappings \(Q:V\rightarrow V\). (English) Zbl 1369.15014 Adv. Appl. Clifford Algebr. 27, No. 2, 1263-1281 (2017). Reviewer: Adam Chapman (Upper Galilee) MSC: 15A66 15A78 15A75 PDFBibTeX XMLCite \textit{J. Helmstetter}, Adv. Appl. Clifford Algebr. 27, No. 2, 1263--1281 (2017; Zbl 1369.15014) Full Text: DOI
Dechant, Pierre-Philippe The \(E_8\) geometry from a Clifford perspective. (English) Zbl 1368.52006 Adv. Appl. Clifford Algebr. 27, No. 1, 397-421 (2017). MSC: 52B10 52B12 52B15 15A66 20F55 17B22 14E16 PDFBibTeX XMLCite \textit{P.-P. Dechant}, Adv. Appl. Clifford Algebr. 27, No. 1, 397--421 (2017; Zbl 1368.52006) Full Text: DOI arXiv
Hitzer, Eckhard General two-sided quaternion Fourier transform, convolution and mustard convolution. (English) Zbl 1368.42009 Adv. Appl. Clifford Algebr. 27, No. 1, 381-395 (2017). MSC: 42B10 PDFBibTeX XMLCite \textit{E. Hitzer}, Adv. Appl. Clifford Algebr. 27, No. 1, 381--395 (2017; Zbl 1368.42009) Full Text: DOI
Anglès, Pierre A few comments on conformal spin structures and conformal \(\mathrm{U}(1)\)-spin structures on a pseudo-Riemannian \(2r\)-dimensional manifold \(V\). (English) Zbl 1426.53067 Adv. Appl. Clifford Algebr. 27, No. 1, 165-183 (2017). MSC: 53C27 11E88 15A66 20G20 PDFBibTeX XMLCite \textit{P. Anglès}, Adv. Appl. Clifford Algebr. 27, No. 1, 165--183 (2017; Zbl 1426.53067) Full Text: DOI
Shirokov, D. S. Method of averaging in Clifford algebras. (English) Zbl 1377.15012 Adv. Appl. Clifford Algebr. 27, No. 1, 149-163 (2017). Reviewer: Jaydeb Sarkar (Bangalore) MSC: 15A66 PDFBibTeX XMLCite \textit{D. S. Shirokov}, Adv. Appl. Clifford Algebr. 27, No. 1, 149--163 (2017; Zbl 1377.15012) Full Text: DOI arXiv
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
Scofield, D. F. Quantum mass-spacetimes – a Clifford and Lie algebraic approach. (English) Zbl 1325.83012 Adv. Appl. Clifford Algebr. 25, No. 3, 673-706 (2015). MSC: 83C45 17B81 PDFBibTeX XMLCite \textit{D. F. Scofield}, Adv. Appl. Clifford Algebr. 25, No. 3, 673--706 (2015; Zbl 1325.83012) Full Text: DOI
Helmstetter, Jacques Factorization of Lipschitzian elements. (English) Zbl 1307.15031 Adv. Appl. Clifford Algebr. 24, No. 3, 675-712 (2014). Reviewer: Dmitri Artamonov (Moskva) MSC: 15A66 15A63 20M32 PDFBibTeX XMLCite \textit{J. Helmstetter}, Adv. Appl. Clifford Algebr. 24, No. 3, 675--712 (2014; Zbl 1307.15031) 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
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
Helmstetter, Jacques; Micali, Artibano; Revoy, Philippe On the definition of quadratic mappings. (English) Zbl 1301.15017 Adv. Appl. Clifford Algebr. 24, No. 1, 125-140 (2014). MSC: 15A63 15A66 11E81 PDFBibTeX XMLCite \textit{J. Helmstetter} et al., Adv. Appl. Clifford Algebr. 24, No. 1, 125--140 (2014; Zbl 1301.15017) Full Text: DOI
Helmstetter, Jacques Mesonic differential forms. (English) Zbl 1301.58001 Adv. Appl. Clifford Algebr. 23, No. 4, 863-886 (2013). Reviewer: Volker Branding (Wien) MSC: 58A10 15A66 15A75 53C99 PDFBibTeX XMLCite \textit{J. Helmstetter}, Adv. Appl. Clifford Algebr. 23, No. 4, 863--886 (2013; Zbl 1301.58001) Full Text: DOI
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
Helmstetter, Jacques Comultiplications with meson algebras. (English) Zbl 1247.15024 Adv. Appl. Clifford Algebr. 21, No. 2, 365-405 (2011). MSC: 15A78 15A63 16S80 81R20 PDFBibTeX XMLCite \textit{J. Helmstetter}, Adv. Appl. Clifford Algebr. 21, No. 2, 365--405 (2011; Zbl 1247.15024) Full Text: DOI
Helmstetter, Jacques Supports and groups in meson algebras. (English) Zbl 1247.15023 Adv. Appl. Clifford Algebr. 21, No. 2, 341-364 (2011). MSC: 15A78 15A63 16S10 PDFBibTeX XMLCite \textit{J. Helmstetter}, Adv. Appl. Clifford Algebr. 21, No. 2, 341--364 (2011; Zbl 1247.15023) Full Text: DOI