February 26, 2024Open Access

On the algebra generated by three commuting matrices: combinatorial cases

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Abstract

Gerstenhaber proved in 1961 that the unital algebra generated by a pair of commuting d d matrices over a field has dimension at most d. It is an open problem whether the analogous statement is true for triples of matrices which pairwise commute. We answer this question for special classes of triples of matrices arising from combinatorial data.

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Cherny et al. (Mon,) studied this question.

synapsesocial.com/papers/68e779e4b6db6435876ee842 https://doi.org/https://doi.org/10.48550/arxiv.2402.16334

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