English

Malcev dialgebras

Rings and Algebras 2011-08-03 v1 Mathematical Physics math.MP Representation Theory

Abstract

We apply Kolesnikov's algorithm to obtain a variety of nonassociative algebras defined by right anticommutativity and a `noncommutative' version of the Malcev identity. We use computational linear algebra to verify that these identities are equivalent to the identities of degree <= 4 satisfied by the dicommutator in every alternative dialgebra. We extend these computations to show that any special identity for Malcev dialgebras must have degree at least 7. Finally, we introduce a trilinear operation which makes any Malcev dialgebra into a Leibniz triple system.

Keywords

Cite

@article{arxiv.1108.0586,
  title  = {Malcev dialgebras},
  author = {Murray R. Bremner and Luiz A. Peresi and Juana Sanchez-Ortega},
  journal= {arXiv preprint arXiv:1108.0586},
  year   = {2011}
}

Comments

16 pages

R2 v1 2026-06-21T18:45:24.577Z