Preprint Review Version 1 Preserved in Portico This version is not peer-reviewed

On Jordan Algebras and Some Unification Results

Version 1 : Received: 7 October 2020 / Approved: 8 October 2020 / Online: 8 October 2020 (09:46:45 CEST)

How to cite: Nichita, F. On Jordan Algebras and Some Unification Results. Preprints 2020, 2020100170 (doi: 10.20944/preprints202010.0170.v1). Nichita, F. On Jordan Algebras and Some Unification Results. Preprints 2020, 2020100170 (doi: 10.20944/preprints202010.0170.v1).

Abstract

This paper is based on a talk given at the 14-th International Workshop on Differential Geometry and Its Applications, hosted by the Petroleum Gas University from Ploiesti, between July 9-th and July 11-th, 2019. After presenting some historical facts, we will consider some geometry problems related to unification approaches. Jordan algebras and Lie algebras are the main non-associative structures. Attempts to unify non-associative algebras and associative algebras led to UJLA structures. Another algebraic structure which unifies non-associative algebras and associative algebras is the Yang-Baxter equation. We will review topics relared to the Yang-Baxter equation and Yang-Baxter systems, with the goal to unify constructions from Differential Geometry.

Subject Areas

Jordan algebras; Lie algebras; associative algebras; Yang-Baxter equations

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