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Malcev dialgebras |
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| Authors: | Murray R Bremner Luiz A Peresi Juana Sánchez-Ortega |
| Institution: | 1. Department of Mathematics and Statistics , University of Saskatchewan , Saskatchewan, 57N 5E6, Canada bremner@math.usask.ca;3. Department of Mathematics , University of S?o Paulo , S?o Paulo , Brazil;4. Department of Algebra, Geometry and Topology , University of Málaga , Malaga , Spain |
| 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. |
| Keywords: | nonassociative algebra computer algebra dialgebras trilinear operations |