On the *-polynomial identities of M-1,M-1(E)

Author(s)

Di Vincenzo, Onofrio M. ; Koshlukov, Plamen

• Document type: Journal article
• Source: Journal of Pure and Applied Algebra; v. 215, n. 3, p. 14-pg., 2011-03-01.

Abstract

In this paper we consider the algebra M-1,M-1(E) endowed with the involution * induced by the transposition superinvolution of the superalgebra M-1,M-1(F) of 2 x 2-matrices over the field F. We study the *-polynomial identities for this algebra in the case of characteristic zero. We describe a finite set generating the ideal of its *-identities. We also consider M-n(E), the algebra of n x n matrices over the Grassmann algebra E. We prove that for a large class of involutions defined on it any *-polynomial identity is indeed a polynomial identity. A similar result holds for the verbally prime algebra M-k,M-l(E). (C) 2010 Elsevier B.V. All rights reserved. (AU)

• FAPESP's process: 05/60337-2 - Lie and Jordan algebras, their representations and generalizations
• Grantee: Ivan Chestakov
• Support Opportunities: Research Projects - Thematic Grants