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

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