On the Algebra Generated by Three Commuting Matrices: Combinatorial Cases
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.
Authors
- Matthew Satriano (ORCID: https://orcid.org/0000-0001-7954-1210)
- Ron Cherny
- Yohan Song
Institutions
- University of Waterloo (CA)
Publication Details
- Journal
- The Electronic Journal of Combinatorics
- Published
- 2024-11-15
- DOI
- https://doi.org/10.37236/12909
- Primary Topic
- Matrix Theory and Algorithms
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Universities Space Research Association
- Natural Sciences and Engineering Research Council of Canada