Carotenuto, Alessandro; Ó Buachalla, Réamonn Bimodule connections for relative line modules over the irreducible quantum flag manifolds. (English) Zbl 07602672 SIGMA, Symmetry Integrability Geom. Methods Appl. 18, Paper 070, 21 p. (2022). MSC: 46L87 81R60 81R50 17B37 16T05 PDF BibTeX XML Cite \textit{A. Carotenuto} and \textit{R. Ó Buachalla}, SIGMA, Symmetry Integrability Geom. Methods Appl. 18, Paper 070, 21 p. (2022; Zbl 07602672) Full Text: DOI arXiv OpenURL
van Suijlekom, Walter D.; Winkel, Jeroen The fundamental group of a noncommutative space. (English) Zbl 07550130 Algebr. Represent. Theory 25, No. 4, 1003-1035 (2022). MSC: 46M20 46L87 PDF BibTeX XML Cite \textit{W. D. van Suijlekom} and \textit{J. Winkel}, Algebr. Represent. Theory 25, No. 4, 1003--1035 (2022; Zbl 07550130) Full Text: DOI arXiv OpenURL
Mathieu, Philippe; Wallet, Jean-Christophe Single extra dimension from \(\kappa\)-Poincaré and gauge invariance. (English) Zbl 1461.81071 J. High Energy Phys. 2021, No. 3, Paper No. 209, 26 p. (2021). MSC: 81T10 83C65 85A25 PDF BibTeX XML Cite \textit{P. Mathieu} and \textit{J.-C. Wallet}, J. High Energy Phys. 2021, No. 3, Paper No. 209, 26 p. (2021; Zbl 1461.81071) Full Text: DOI arXiv OpenURL
Dubois-Violette, Michel; Todorov, Ivan Superconnection in the spin factor approach to particle physics. (English) Zbl 1473.81243 Nucl. Phys., B 957, Article ID 115065, 15 p. (2020). MSC: 81V22 81V74 17A15 17C90 PDF BibTeX XML Cite \textit{M. Dubois-Violette} and \textit{I. Todorov}, Nucl. Phys., B 957, Article ID 115065, 15 p. (2020; Zbl 1473.81243) Full Text: DOI arXiv OpenURL
Nguyen, Hans; Schenkel, Alexander Dirac operators on noncommutative hypersurfaces. (English) Zbl 1450.81048 J. Geom. Phys. 158, Article ID 103917, 19 p. (2020). MSC: 81R60 81Q10 81R25 58B34 53C27 46L87 PDF BibTeX XML Cite \textit{H. Nguyen} and \textit{A. Schenkel}, J. Geom. Phys. 158, Article ID 103917, 19 p. (2020; Zbl 1450.81048) Full Text: DOI arXiv OpenURL
Mathieu, Philippe; Wallet, Jean-Christophe Gauge theories on \(\kappa\)-Minkowski spaces: twist and modular operators. (English) Zbl 1437.83041 J. High Energy Phys. 2020, No. 5, Paper No. 112, 31 p. (2020). MSC: 83C45 83C65 81Q10 PDF BibTeX XML Cite \textit{P. Mathieu} and \textit{J.-C. Wallet}, J. High Energy Phys. 2020, No. 5, Paper No. 112, 31 p. (2020; Zbl 1437.83041) Full Text: DOI arXiv OpenURL
D’Andrea, Francesco On the notion of noncommutative submanifold. (English) Zbl 1454.46074 SIGMA, Symmetry Integrability Geom. Methods Appl. 16, Paper 050, 21 p. (2020). MSC: 46L87 53C99 53D55 13N15 PDF BibTeX XML Cite \textit{F. D'Andrea}, SIGMA, Symmetry Integrability Geom. Methods Appl. 16, Paper 050, 21 p. (2020; Zbl 1454.46074) Full Text: DOI arXiv OpenURL
Abramov, Viktor; Liivapuu, Olga Connections in Euclidean and non-commutative geometry. (English) Zbl 1442.58009 Bernstein, Swanhild (ed.), Topics in Clifford analysis. Special volume in honor of Wolfgang Sprößig on the occasion of his 70th birthday. Cham: Birkhäuser. Trends Math., 279-311 (2019). Reviewer: Savin Treanta (Bucharest) MSC: 58C50 53A40 PDF BibTeX XML Cite \textit{V. Abramov} and \textit{O. Liivapuu}, in: Topics in Clifford analysis. Special volume in honor of Wolfgang Sprößig on the occasion of his 70th birthday. Cham: Birkhäuser. 279--311 (2019; Zbl 1442.58009) Full Text: DOI OpenURL
Carotenuto, Alessandro; Dąbrowski, Ludwik; Dubois-Violette, Michel Differential calculus on Jordan algebras and Jordan modules. (English) Zbl 1452.17029 Lett. Math. Phys. 109, No. 1, 113-133 (2019). Reviewer: Aubrey Wulfsohn (Coventry) MSC: 17C40 17C36 17C90 46C99 PDF BibTeX XML Cite \textit{A. Carotenuto} et al., Lett. Math. Phys. 109, No. 1, 113--133 (2019; Zbl 1452.17029) Full Text: DOI arXiv OpenURL
Marmo, Giuseppe; Vitale, Patrizia; Zampini, Alessandro Derivation based differential calculi for noncommutative algebras deforming a class of three dimensional spaces. (English) Zbl 1420.46050 J. Geom. Phys. 136, 104-118 (2019). MSC: 46L87 58J42 PDF BibTeX XML Cite \textit{G. Marmo} et al., J. Geom. Phys. 136, 104--118 (2019; Zbl 1420.46050) Full Text: DOI arXiv OpenURL
Dubois-Violette, Michel; Todorov, Ivan Exceptional quantum geometry and particle physics. II. (English) Zbl 1405.81167 Nucl. Phys., B 938, 751-761 (2019). MSC: 81V05 81V15 81V22 17C40 11R52 15A66 PDF BibTeX XML Cite \textit{M. Dubois-Violette} and \textit{I. Todorov}, Nucl. Phys., B 938, 751--761 (2019; Zbl 1405.81167) Full Text: DOI arXiv OpenURL
Brzeziński, Tomasz Differential and integral forms on non-commutative algebras. (English) Zbl 1403.58005 Kielanowski, Piotr (ed.) et al., Geometric methods in physics XXXV. Workshop and summer school, Białowieża, Poland, June 26 – July 2, 2016. Cham: Birkhäuser (ISBN 978-3-319-63593-4/hbk; 978-3-319-63594-1/ebook). Trends in Mathematics, 257-261 (2018). MSC: 58B32 58B34 PDF BibTeX XML Cite \textit{T. Brzeziński}, in: Geometric methods in physics XXXV. Workshop and summer school, Białowieża, Poland, June 26 -- July 2, 2016. Cham: Birkhäuser. 257--261 (2018; Zbl 1403.58005) Full Text: DOI arXiv OpenURL
Feizabadi, Hassan; Boroojerdian, Naser Extending tangent bundles by an algebra bundle. (English) Zbl 1397.58002 Iran. J. Sci. Technol., Trans. A, Sci. 42, No. 2, 615-621 (2018). MSC: 58A32 53C15 PDF BibTeX XML Cite \textit{H. Feizabadi} and \textit{N. Boroojerdian}, Iran. J. Sci. Technol., Trans. A, Sci. 42, No. 2, 615--621 (2018; Zbl 1397.58002) Full Text: DOI OpenURL
Boyle, Latham; Farnsworth, Shane A new algebraic structure in the standard model of particle physics. (English) Zbl 1395.83072 J. High Energy Phys. 2018, No. 6, Paper No. 71, 32 p. (2018). MSC: 83C65 81T13 83C60 15A72 PDF BibTeX XML Cite \textit{L. Boyle} and \textit{S. Farnsworth}, J. High Energy Phys. 2018, No. 6, Paper No. 71, 32 p. (2018; Zbl 1395.83072) Full Text: DOI arXiv OpenURL
Jurić, Tajron; Poulain, Timothé; Wallet, Jean-Christophe Involutive representations of coordinate algebras and quantum spaces. (English) Zbl 1380.83095 J. High Energy Phys. 2017, No. 7, Paper No. 116, 32 p. (2017). MSC: 83C45 83C27 81T25 17B45 PDF BibTeX XML Cite \textit{T. Jurić} et al., J. High Energy Phys. 2017, No. 7, Paper No. 116, 32 p. (2017; Zbl 1380.83095) Full Text: DOI arXiv OpenURL
Aguillón, Cesar A.; Much, Albert; Rosenbaum, Marcos; Vergara, J. David Noncommutative Riemannian geometry from quantum spacetime generated by twisted Poincaré group. (English) Zbl 1386.83095 J. Math. Phys. 58, No. 11, 112301, 27 p. (2017). MSC: 83C65 83C45 58B34 53C28 53D55 12H05 16D20 PDF BibTeX XML Cite \textit{C. A. Aguillón} et al., J. Math. Phys. 58, No. 11, 112301, 27 p. (2017; Zbl 1386.83095) Full Text: DOI OpenURL
Zahariev, Svetoslav Curved \(A_{\infty }\)-algebras and gauge theory. (English) Zbl 1425.70043 J. Homotopy Relat. Struct. 12, No. 1, 1-15 (2017). MSC: 70S15 16E45 18G55 PDF BibTeX XML Cite \textit{S. Zahariev}, J. Homotopy Relat. Struct. 12, No. 1, 1--15 (2017; Zbl 1425.70043) Full Text: DOI arXiv OpenURL
Tacchella, Alberto An introduction to associative geometry with applications to integrable systems. (English) Zbl 1382.16015 J. Geom. Phys. 118, 202-233 (2017). MSC: 16S10 16E45 14A22 14H70 16S38 46L87 PDF BibTeX XML Cite \textit{A. Tacchella}, J. Geom. Phys. 118, 202--233 (2017; Zbl 1382.16015) Full Text: DOI arXiv OpenURL
Jurić, Tajron; Poulain, Timothé; Wallet, Jean-Christophe Closed star product on noncommutative \(\mathbb R^{3}\) and scalar field dynamics. (English) Zbl 1388.83538 J. High Energy Phys. 2016, No. 5, Paper No. 146, 22 p. (2016). MSC: 83C65 53D55 PDF BibTeX XML Cite \textit{T. Jurić} et al., J. High Energy Phys. 2016, No. 5, Paper No. 146, 22 p. (2016; Zbl 1388.83538) Full Text: DOI arXiv OpenURL
Franco, Nicolas; Wallet, Jean-Christophe Metrics and causality on Moyal planes. (English) Zbl 1365.58005 Martinetti, Pierre (ed.) et al., Noncommutative geometry and optimal transport. Workshop on noncommutative geometry and optimal transport, Besançon, France, November 27, 2014. Providence, RI: American Mathematical Society (AMS) (ISBN 978-1-4704-2297-4/pbk; 978-1-4704-3560-8/ebook). Contemporary Mathematics 676, 147-173 (2016). Reviewer: Iakovos Androulidakis (Athína) MSC: 58B34 54E35 53C50 54F05 PDF BibTeX XML Cite \textit{N. Franco} and \textit{J.-C. Wallet}, Contemp. Math. 676, 147--173 (2016; Zbl 1365.58005) Full Text: DOI arXiv OpenURL
Dubois-Violette, Michel Exceptional quantum geometry and particle physics. (English) Zbl 1349.81179 Nucl. Phys., B 912, 426-449 (2016). MSC: 81V05 81V15 81V22 17C40 11R52 PDF BibTeX XML Cite \textit{M. Dubois-Violette}, Nucl. Phys., B 912, 426--449 (2016; Zbl 1349.81179) Full Text: DOI arXiv OpenURL
Wallet, Jean-Christophe Exact partition functions for gauge theories on \(\mathbb{R}_\lambda^3\). (English) Zbl 1349.81173 Nucl. Phys., B 912, 354-373 (2016). MSC: 81T75 81T13 81T15 58B34 37K10 PDF BibTeX XML Cite \textit{J.-C. Wallet}, Nucl. Phys., B 912, 354--373 (2016; Zbl 1349.81173) Full Text: DOI arXiv OpenURL
Barnes, Gwendolyn E.; Schenkel, Alexander; Szabo, Richard J. Nonassociative geometry in quasi-Hopf representation categories. II: Connections and curvature. (English) Zbl 1342.83220 J. Geom. Phys. 106, 234-255 (2016). MSC: 83C65 81T20 83C45 83D05 16T05 17B37 46L87 53D55 PDF BibTeX XML Cite \textit{G. E. Barnes} et al., J. Geom. Phys. 106, 234--255 (2016; Zbl 1342.83220) Full Text: DOI arXiv OpenURL
Géré, Antoine; Jurić, Tajron; Wallet, Jean-Christophe Noncommutative gauge theories on \( {{\mathbb{R}}}_{\lambda}^3 \): perturbatively finite models. (English) Zbl 1387.81266 J. High Energy Phys. 2015, No. 12, Paper No. 45, 29 p. (2015). MSC: 81T13 83C65 83C45 PDF BibTeX XML Cite \textit{A. Géré} et al., J. High Energy Phys. 2015, No. 12, Paper No. 45, 29 p. (2015; Zbl 1387.81266) Full Text: DOI arXiv OpenURL
Jurić, Tajron; Meljanac, Stjepan; Pikutić, Danijel; Štrajn, Rina Toward the classification of differential calculi on \(\kappa\)-Minkowski space and related field theories. (English) Zbl 1388.83537 J. High Energy Phys. 2015, No. 7, Paper No. 55, 33 p. (2015). MSC: 83C65 PDF BibTeX XML Cite \textit{T. Jurić} et al., J. High Energy Phys. 2015, No. 7, Paper No. 55, 33 p. (2015; Zbl 1388.83537) Full Text: DOI arXiv OpenURL
Chakraborty, Partha Sarathi; Guin, Satyajit Noncommutative differential calculus on a quadratic algebra. (English) Zbl 1355.46059 Indian J. Pure Appl. Math. 46, No. 4, 495-515 (2015). Reviewer: Igor V. Nikolaev (New York) MSC: 46L85 PDF BibTeX XML Cite \textit{P. S. Chakraborty} and \textit{S. Guin}, Indian J. Pure Appl. Math. 46, No. 4, 495--515 (2015; Zbl 1355.46059) Full Text: DOI OpenURL
Barnes, Gwendolyn E.; Schenkel, Alexander; Szabo, Richard J. Nonassociative geometry in quasi-Hopf representation categories. I: Bimodules and their internal homomorphisms. (English) Zbl 1321.83035 J. Geom. Phys. 89, 111-152 (2015). MSC: 83C65 81T20 83C45 16T05 17B37 46L87 53D55 PDF BibTeX XML Cite \textit{G. E. Barnes} et al., J. Geom. Phys. 89, 111--152 (2015; Zbl 1321.83035) Full Text: DOI arXiv OpenURL
Zampini, Alessandro Warped products and Yang-Mills equations on noncommutative spaces. (English) Zbl 1309.53028 Lett. Math. Phys. 105, No. 2, 221-243 (2015). MSC: 53C07 81R60 17B37 PDF BibTeX XML Cite \textit{A. Zampini}, Lett. Math. Phys. 105, No. 2, 221--243 (2015; Zbl 1309.53028) Full Text: DOI arXiv OpenURL
Maeda, Yoshiaki; Sako, Akifumi; Suzuki, Toshiya; Umetsu, Hiroshi Gauge theories in noncommutative homogeneous Kähler manifolds. (English) Zbl 1306.81304 J. Math. Phys. 55, No. 9, 092301, 17 p. (2014). Reviewer: Ahmed Hegazi (Mansoura) MSC: 81T75 81T13 32Q15 81S10 53D55 PDF BibTeX XML Cite \textit{Y. Maeda} et al., J. Math. Phys. 55, No. 9, 092301, 17 p. (2014; Zbl 1306.81304) Full Text: DOI arXiv OpenURL
Dubois-Violette, Michel; Landi, Giovanni The Weil algebra of a Hopf algebra. I: A noncommutative framework. (English) Zbl 1315.81049 Commun. Math. Phys. 326, No. 3, 851-874 (2014). MSC: 81R05 81R10 81R60 PDF BibTeX XML Cite \textit{M. Dubois-Violette} and \textit{G. Landi}, Commun. Math. Phys. 326, No. 3, 851--874 (2014; Zbl 1315.81049) Full Text: DOI arXiv OpenURL
de Goursac, Axel; Masson, Thierry; Wallet, Jean-Christophe Noncommutative \(\varepsilon \)-graded connections. (English) Zbl 1275.58003 J. Noncommut. Geom. 6, No. 2, 343-387 (2012). Reviewer: Akira Asada (Takarazuka) MSC: 58B34 17B75 46L87 81T75 81T13 PDF BibTeX XML Cite \textit{A. de Goursac} et al., J. Noncommut. Geom. 6, No. 2, 343--387 (2012; Zbl 1275.58003) Full Text: DOI arXiv OpenURL
Cagnache, Eric; Masson, Thierry; Wallet, Jean-Christophe Noncommutative Yang-Mills-Higgs actions from derivation-based differential calculus. (English) Zbl 1226.81279 J. Noncommut. Geom. 5, No. 1, 39-67 (2011). Reviewer: Saeid Jafari (Copenhagen) MSC: 81T75 81T13 81T15 PDF BibTeX XML Cite \textit{E. Cagnache} et al., J. Noncommut. Geom. 5, No. 1, 39--67 (2011; Zbl 1226.81279) Full Text: DOI arXiv OpenURL
Beggs, E. J.; Majid, S. *-compatible connections in noncommutative Riemannian geometry. (English) Zbl 1211.53092 J. Geom. Phys. 61, No. 1, 95-124 (2011). MSC: 53C80 53C20 58J42 PDF BibTeX XML Cite \textit{E. J. Beggs} and \textit{S. Majid}, J. Geom. Phys. 61, No. 1, 95--124 (2011; Zbl 1211.53092) Full Text: DOI arXiv OpenURL
Brzeziński, Tomasz; El Kaoutit, Laiachi; Lomp, Christian Non-commutative integral forms and twisted multi-derivations. (English) Zbl 1186.58005 J. Noncommut. Geom. 4, No. 2, 281-312 (2010). MSC: 58B32 16W25 PDF BibTeX XML Cite \textit{T. Brzeziński} et al., J. Noncommut. Geom. 4, No. 2, 281--312 (2010; Zbl 1186.58005) Full Text: DOI arXiv Link OpenURL
Morchio, G.; Strocchi, F. Classical and quantum mechanics from the universal Poisson-Rinehart algebra of a manifold. (English) Zbl 1204.81103 Rep. Math. Phys. 64, No. 1-2, 33-48 (2009). MSC: 81S10 17B63 53D17 70H40 81Q70 PDF BibTeX XML Cite \textit{G. Morchio} and \textit{F. Strocchi}, Rep. Math. Phys. 64, No. 1--2, 33--48 (2009; Zbl 1204.81103) Full Text: DOI arXiv OpenURL
Nikonov, I. M. Universal Karoubi characteristic classes of nuclear \(C^*\)-algebras. (English. Russian original) Zbl 1188.46047 J. Math. Sci., New York 159, No. 6, 837-862 (2009); translation from Fundam. Prikl. Mat. 13, No. 8, 133-169 (2007). MSC: 46L87 46L80 46L35 PDF BibTeX XML Cite \textit{I. M. Nikonov}, J. Math. Sci., New York 159, No. 6, 837--862 (2009; Zbl 1188.46047); translation from Fundam. Prikl. Mat. 13, No. 8, 133--169 (2007) Full Text: DOI OpenURL
Morchio, Giovanni; Strocchi, Franco The Lie-Rinehart universal Poisson algebra of classical and quantum mechanics. (English) Zbl 1175.81135 Lett. Math. Phys. 86, No. 2-3, 135-150 (2008). MSC: 81S10 81Q70 81R15 53D17 81R60 81R10 70G45 PDF BibTeX XML Cite \textit{G. Morchio} and \textit{F. Strocchi}, Lett. Math. Phys. 86, No. 2--3, 135--150 (2008; Zbl 1175.81135) Full Text: DOI arXiv OpenURL
Connes, Alain; Dubois-Violette, Michel Noncommutative finite dimensional manifolds. II: Moduli space and structure of noncommutative 3-spheres. (English) Zbl 1159.58003 Commun. Math. Phys. 281, No. 1, 23-127 (2008). MSC: 58B34 46L87 PDF BibTeX XML Cite \textit{A. Connes} and \textit{M. Dubois-Violette}, Commun. Math. Phys. 281, No. 1, 23--127 (2008; Zbl 1159.58003) Full Text: DOI arXiv OpenURL
Giunashvili, Z. Noncommutative geometry of Poisson structures. (English. Russian original) Zbl 1146.53056 J. Math. Sci., New York 141, No. 2, 1091-1112 (2007); translation from Sovrem. Mat. Prilozh. 27, 3-24 (2005). MSC: 53D17 58B34 17B63 17B56 PDF BibTeX XML Cite \textit{Z. Giunashvili}, J. Math. Sci., New York 141, No. 2, 1091--1112 (2007; Zbl 1146.53056); translation from Sovrem. Mat. Prilozh. 27, 3--24 (2005) Full Text: DOI OpenURL