Identities of metabelian alternative algebras

Abstract

We study metabelian alternative (in particular, associative) algebras over a field of characteristic 0. We construct additive bases of the free algebras of mentioned varieties, describe some centers of these algebras, compute the values of the sequence of codimensions of corresponding T-ideals, and find unitarily irreducible components of the decomposition of mentioned varieties into a union and their bases of identities. In particular, we find a basis of identities for the metabelian alternative Grassmann algebra. We prove that the free algebra of a variety that is generated by the metabelian alternative Grassmann algebra possesses the zero associative center.