On the graded automorphisms of upper triangular matrix algebras
Felipe Yukihide Yasumura

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.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Matrix Theory and Algorithms
