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.
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