Representations of Generalized Almost-Jordan algebras

Abstract

This paper deals with the variety of commutative algebras satisfying one of the four families of degree four identities found by Carini, Hentzel and Piacentini-Cattaneo in 1988. We give a characterization of representations and irreducible modules on these algebras. Our results require that the characteristic of the ground field be different from 2,3.