Graded Isomorphisms on Upper Block Triangular Matrix Algebras

TL;DR

This paper characterizes graded isomorphisms of endomorphism rings of graded flags and classifies upper block triangular matrix algebras graded by finite abelian groups over algebraically closed fields.

Contribution

It provides a complete description of graded isomorphisms and classifies graded upper block triangular matrix algebras, extending understanding of their structure.

Findings

Classification of graded isomorphisms of endomorphism rings

Description of isomorphism classes of graded upper block triangular matrices

Application to algebras over algebraically closed fields of characteristic zero

Abstract

We describe the graded isomorphisms of rings of endomorphisms of graded flags over graded division algebras. As a consequence describe the isomorphism classes of upper block triangular matrix algebras (over an algebraically closed field of characteristic zero) graded by a finite abelian group.