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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 computer algebra to verify that these identities are equivalent to the identities of degree up to 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.
Acknowledgements
The authors thank Alexander Pozhidaev for helpful comments, and Pavel Kolesnikov for references Citation3,Citation16. Murray Bremner was supported by a Discovery Grant from NSERC; he thanks the Department of Algebra, Geometry and Topology at the University of Málaga for its hospitality during his visit in June and July 2011. Luiz Peresi was supported by CNPq of Brazil. Juana Sánchez-Ortega was supported by the Spanish MEC and Fondos FEDER jointly through project MTM2010-15223, and by the Junta de Andalucía (projects FQM-336 and FQM2467).