Representations of Generalized Almost-Jordan Algebras

Abstract

This paper deals with the variety of commutative algebras satisfying the identity {(yx2)x − ((yx)x)x} + {yx3 − ((yx)x)x} = 0 where , are scalars. These algebras appeared as one of the four fam- ilies of degree four identities in Carini, Hentzel and Piacentini-Cattaneo [6]. We give a characterization of representations and irreducible mod- ules on these algebras. Our results require that the characteristic of the ground field was different from 2, 3.