The matrix Lie algebra on a one-step ladder is zero product determined

TL;DR

This paper proves that matrix algebras on a one-step ladder are zero product determined when considering the Lie bracket, extending previous results from matrix multiplication.

Contribution

It establishes that the matrix algebra on a one-step ladder is zero product determined under the Lie bracket, a novel extension of prior work on matrix multiplication.

Findings

Matrix algebra on a one-step ladder is zero product determined under the Lie bracket.

Extends previous results from matrix multiplication to Lie algebra context.

Provides new insights into algebraic structures on ladders.

Abstract

The class of matrix algebras on a ladder $\mathcal{L}$ generalizes the class of block upper triangular matrix algebras. It was previously shown that the matrix algebra on a ladder $\mathcal{L}$ is zero product determined under matrix multiplication. In this article, we show that the matrix algebra on a one-step ladder is zero product determined under the Lie bracket.