Ordinary and ℤ2-Graded Cocharacters of UT 2(E)

Abstract

Let E be the infinite dimensional Grassmann algebra over a field F of characteristic 0. In this article we consider the algebra R of 2 × 2 matrices with entries in E and its subalgebra G, which is one of the minimal algebras of polynominal identity (PI) exponent 2. We compute firstly the Hilbert series of G and, as a consequence, we compute its cocharacter sequence. Then we find the Hilbert series of R, using the tool of proper Hilbert series, and we compute its cocharacter sequence. Finally we describe explicitely the ℤ2-graded cocharacters of R.