Ordinary and Z/2Z-graded Cocharacters of UT_2(E)

TL;DR

This paper computes the ordinary and Z/2Z-graded cocharacters of the algebra of 2x2 upper triangular matrices over an infinite dimensional Grassmann algebra, utilizing proper Hilbert series as a key tool.

Contribution

It introduces a method to determine cocharacters of this algebra using proper Hilbert series, providing new insights into its polynomial identities.

Findings

Explicit formulas for cocharacters obtained

Enhanced understanding of polynomial identities in graded algebras

Method applicable to similar algebraic structures

Abstract

Let E be the infinite dimensional Grassmann algebra over a field F of characteristic 0. In this paper we compute the ordinary and the Z/2Z-graded cocharacters of the algebra of 2x2 upper triangular matrices with coefficients in E, using the tool of proper Hilbert series.