Representations of Generalized Almost-Jordan Algebras

Abstract

This paper deals with the variety of commutative algebras satisfying the identity β{(yx ²)x − ((yx)x)x} + γ{yx ³ − ((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.

Key Words:

• Irreducible module
• Linearization
• Representation
• Variety

2010 Mathematics Subject Classification:

• 17A30
• 17C50

ACKNOWLEDGMENT

The authors thanks the referee for his/her valuable suggestions and comments that improve the presentation of this paper.

Notes

Communicated by I. Shestakov.