2011/08/02 by Bremner, Murray R., Peresi, Luiz A., Sanchez-Ortega, Juana
#17A32 #17D10 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Representation Theory (math.RT) #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.1108.0586
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.