Symmetrization of Jordan dialgebras
Abstract
A basic problem for any class of nonassociative algebras is to determine the polynomial identities satisfied by the symmetrization and the skewsymmetrization of the original product. We consider the symmetrization of the product in the class of special Jordan dialgebras. We use computational linear algebra to show that every polynomial identity of degree $n \le 5$ satisfied by the symmetrized Jordan diproduct in every diassociative algebra is a consequence of commutativity. We determine a complete set of generators for the polynomial identities in degree 6 which are not consequences of commutativity. We use a constructive version of the representation theory of the symmetric group to show that there exist further new identities in degree 7.
 Publication:

arXiv eprints
 Pub Date:
 January 2018
 arXiv:
 arXiv:1802.00039
 Bibcode:
 2018arXiv180200039B
 Keywords:

 Mathematics  Rings and Algebras;
 Mathematics  Representation Theory;
 17A30 (Primary) 16W10;
 17A50;
 17C05;
 17C50;
 18D50;
 68W30 (Secondary)
 EPrint:
 12 pages, 8 figures