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arXiv · 1108.0586

Malcev dialgebras

Murray R. Bremner·Luiz A. Peresi·Juana Sanchez-Ortega
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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.

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Murray R. Bremner, Luiz A. Peresi, Juana Sanchez-Ortega. 2011-08-02. Malcev dialgebras. https://arxiv.org/abs/1108.0586

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