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On the algebra generated by three commuting matrices: combinatorial cases (2402.16334v1)
Published 26 Feb 2024 in math.AC, math.CO, and math.OA
Abstract: Gerstenhaber proved in 1961 that the unital algebra generated by a pair of commuting $d\times d$ 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.