Embeddings for the Jordan algebra of a bilinear form

Author(s)

Diniz, Diogo ^[2] ; Koshlukov, Plamen ^[2]

Affiliation

^[1] Univ Fed Campina Grande, Unidade Acad Matemat, BR-58429970 Campina Grande, PB - Brazil

^[2] Univ Estadual Campinas, Dept Math, BR-13083859 Campinas, SP - Brazil

• Document type: Journal article
• Source: ADVANCES IN MATHEMATICS; v. 337, p. 294-316, OCT 15 2018.
• Web of Science Citations: 0

Abstract

Let K be a field of characteristic zero and let J be a Jordan algebra with a formal trace. We prove that the algebra J can be embedded into a Jordan algebra of a non-degenerate symmetric bilinear form over some associative and commutative K-algebra C if and only if J satisfies all trace identities of the Jordan algebra of a non-degenerate symmetric bilinear form over the field K. This is an extension of results of Procesi and Berele concerning the analogous problem for the associative matrix algebras and the matrix algebras with involution. As a consequence of these results we also prove that the ideal of all trace identities of the Jordan algebra of a non-degenerate symmetric bilinear form over K satisfies the Specht property. (C) 2018 Elsevier Inc. All rights reserved. (AU)

• FAPESP's process: 14/09310-5 - Algebraic structures and their representations
• Grantee: Vyacheslav Futorny
• Support Opportunities: Research Projects - Thematic Grants