On the algebra generated by three commuting matrices: combinatorial cases
Commutative Algebra
2024-02-27 v1 Combinatorics
Operator Algebras
Abstract
Gerstenhaber proved in 1961 that the unital algebra generated by a pair of commuting matrices over a field has dimension at most . 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.
Keywords
Cite
@article{arxiv.2402.16334,
title = {On the algebra generated by three commuting matrices: combinatorial cases},
author = {Ron Cherny and Matthew Satriano and Yohan Song},
journal= {arXiv preprint arXiv:2402.16334},
year = {2024}
}