Lett Math Phys https://doi.org/10.1007/s11005-018-1102-z Differential calculus on Jordan algebras and Jordan modules 1 1 Alessandro Carotenuto · Ludwik Dabrowski · Michel Dubois-Violette Received: 29 March 2018 / Revised: 16 May 2018 / Accepted: 17 May 2018 © Springer Science+Business Media B.V., part of Springer Nature 2018 Abstract Having in mind applications to particle physics we develop the differen- tial calculus over Jordan algebras and the theory of connections on Jordan modules. In particular we focus on differential calculus over the exceptional Jordan algebra and provide a complete characterization of the theory of connections for free Jordan modules. Keywords Jordan algebras · Jordan modules · Differential calculus · Connections Mathematics Subject Classiﬁcation 17Cxx · 97140 1 Introduction It is quite legitimate to expect that the ﬁnite spectrum of fundamental particles of matter (fundamental fermions) corresponds to representations of some ﬁnite quantum space. Such a virtual space should be described by its observables, i.e. a quantum analogue of some class of real functions over it. This is of course at the core of B Michel Dubois-Violette firstname.lastname@example.org Alessandro Carotenuto email@example.com Ludwik Da˛browski firstname.lastname@example.org Scuola Internazionale Superiore di Studi Avanzati (SISSA), Via Bonomea 265, 34136 Trieste, Italy Laboratoire de Physique Théorique, CNRS,
Letters in Mathematical Physics – Springer Journals
Published: Jun 5, 2018
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