Differential calculus on Jordan algebras and Jordan modules

DOI10.1007/s11005-018-1102-zzbMath1452.17029arXiv1803.08373OpenAlexW3099609553MaRDI QIDQ1731135

Michel Dubois-Violette, Ludwik Dąbrowski, Alessandro Carotenuto

Publication date: 20 March 2019

Published in: Letters in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1803.08373

zbMATH Keywords

Lie algebrasJordan algebrasrelativistic quantum mechanicselementary particlesdifferential algebrasdifferential Riemannian manifolds

Mathematics Subject Classification ID

Exceptional Jordan structures (17C40) Inner product spaces and their generalizations, Hilbert spaces (46C99) Applications of Jordan algebras to physics, etc. (17C90) Associated manifolds of Jordan algebras (17C36)

Related Items (7)

Superconnection in the spin factor approach to particle physics ⋮ Particle models from special Jordan backgrounds and spectral triples ⋮ The factorization problem for Jordan algebras: applications ⋮ The geometry of physical observables ⋮ Left-covariant first order differential calculus on quantum Hopf supersymmetry algebra ⋮ Unified products for Jordan algebras. Applications ⋮ Jordan algebraic interpretation of maximal parabolic subalgebras: exceptional Lie algebras

Cites Work

• Exceptional quantum geometry and particle physics
• Representation type of Jordan algebras
• Derivations of Jordan algebras
• Moufang plane and octonionic quantum mechanics
• Lie-Rinehart algebras, Gerstenhaber algebras and Batalin-Vilkovisky algebras
• The spectral action principle
• A taste of Jordan algebras
• Differential calculus on compact matrix pseudogroups (quantum groups)
• Noncommutative geometry and particle physics
• Classical bosons in a non-commutative geometry
• Classification of simple z-graded lie superalgebras and simple jordan superalgebras
• Tensor Products of Jordan Algebras
• The octonions
• Differential Forms on General Commutative Algebras
• General Representation Theory of Jordan Algebras
• Particle models and noncommutative geometry
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