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arXiv · 2511.22092

On combinatorial algebras generated by three commuting matrices

Ron Cherny·Tam An Le Quang·Matthew Satriano
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Abstract

Motzkin and Taussky (and independently, Gerstenhaber) proved that the unital algebra generated by a pair of commuting $d\times d$ matrices over a field has dimension at most $d$. Since then, it has remained an open problem to determine whether the analogous statement is true for triples of matrices which pairwise commute. We answer this question for combinatorially-motivated classes of such triples.

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Ron Cherny, Tam An Le Quang, Matthew Satriano. 2025-11-27. On combinatorial algebras generated by three commuting matrices. https://arxiv.org/abs/2511.22092

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