On the graded automorphisms of upper triangular matrix algebras

TL;DR

This paper characterizes the graded automorphisms of upper triangular matrix algebras across associative, Lie, and Jordan structures, including their self-equivalences and symmetry groups.

Contribution

It provides a comprehensive computation of automorphisms and symmetry groups for all gradings of upper triangular matrix algebras, extending previous understanding.

Findings

Explicit descriptions of graded automorphisms for each algebra type

Calculation of self-equivalences and Weyl groups

Identification of diagonal groups for all gradings

Abstract

We compute the graded automorphisms of the upper triangular matrices, viewed as associative, Lie and Jordan algebras. We compute also the so called self-equivalences and Weyl and diagonal groups for every grading.