Representations of Generalized Almost-Jordan Algebras

Abstract

© 2015, Copyright Taylor & Francis Group, LLC. This paper deals with the variety of commutative algebras satisfying the identity β{(yx <sup>2</sup>)x − ((yx)x)x} + γ{yx <sup>3</sup> − ((yx)x)x} = 0, where β, γ are scalars. These algebras appeared as one of the four families of degree four identities in Carini, Hentzel, and Piacentini-Cattaneo [6]. We give a characterization of representations and irreducible modules on these algebras. Our results require that the characteristic of the ground field is different from 2, 3.