# Symmetrization of Jordan dialgebras

@article{Bremner2019SymmetrizationOJ, title={Symmetrization of Jordan dialgebras}, author={Murray R. Bremner}, journal={Nonassociative Mathematics and its Applications}, year={2019} }

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 set of generators for the polynomial identities in degree 6 which do not follow from commutativity. We use the representation theory of the symmetric group to show that there exist further new identities in degree 7.

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