$\sigma$-matching and interchangeable structures on the strictly upper triangular matrix algebra

TL;DR

This paper introduces $\sigma$-matching and interchangeable structures on the algebra of strictly upper triangular matrices, providing new insights into their compatibility and algebraic properties.

Contribution

It defines and analyzes $\sigma$-matching and interchangeable structures on $UT_n(K)$, expanding understanding of their compatibility and algebraic framework.

Findings

Defined $\sigma$-matching and interchangeable structures.

Proved total compatibility of these structures.

Applied results to the algebra of strictly upper triangular matrices.

Abstract

We describe $\sigma$-matching, interchangeable and, as a consequence, totally compatible structures on the strictly upper triangular matrix algebra $UT_n(K)$ for all $n\ge 3$.