A model for the relatively free graded algebra of block triangular matrices with entries from a graded algebra

TL;DR

This paper constructs a model for the relative free G-graded algebra of block triangular matrices over a G-graded algebra satisfying a polynomial identity, revealing a factoring property for T_G-ideals in specific cases.

Contribution

It introduces a new model for the relative free G-graded algebra of block triangular matrices with entries from a G-graded algebra satisfying a polynomial identity.

Findings

Established a factoring property for T_G-ideals in block triangular matrices.

Provided a construction for the relative free G-graded algebra.

Applied the model to matrices over a finite dimensional Grassmann algebra.

Abstract

Let G be a group and A be a G-graded algebra satisfying a polynomial identity. We buid up a model for the relative free G-graded algebra and we obtain, as an application, the "factoring" property for the T_G-ideals of block triangular matrices with entries from the finite dimensional Grassmann algebra E for some particular Z_2-grading.