Symmetrization of Jordan dialgebras

@article{Bremner2019SymmetrizationOJ,
  title={Symmetrization of Jordan dialgebras},
  author={Murray R. Bremner},
  journal={Nonassociative Mathematics and its
                    Applications},
  year={2019}
}
  • M. Bremner
  • Published 31 January 2018
  • Mathematics
  • Nonassociative Mathematics and its Applications
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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