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arxiv: 1108.0586 · v1 · pith:UUWQFB5Onew · submitted 2011-08-02 · 🧮 math.RA · math-ph· math.MP· math.RT

Malcev dialgebras

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keywords malcevdegreedialgebradialgebrasidentitiesidentityalgebraalgebras
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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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