Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
10144938 | Advances in Mathematics | 2018 | 23 Pages |
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Claudemir Fidelis, Diogo Diniz, Plamen Koshlukov,