Some thoughts on Gerstenhaber's theorem
type: Item
instance of: scholarly article
title: Some thoughts on Gerstenhaber's theorem
zbMATH Open document ID: 1301.13022
author: J. Herrera
author: Sumit K. Garg
published in: Linear Algebra and its Applications
publication date: 2014-11-19T00:00:00Z
review text: The paper under review aims at rekindling the interest in extensions of Gerstenhaber's theorem from two commuting matrices to three commuting matrices. The authors mainly discuss possible answers to the question: Must the (unital) subalgebra \(F[A, B, C]\) generated by matrices \(A, B, C\in M_n(F)\) over a field \(F\) have dimension at most \(n\)? For fields of characteristic zero, it is known to be true for \(n\leq 11\) but fails when \(n\geq 29\). A discussion is made on how the gap for \(12\leq n \leq 28\) can be closed. Other situations for which the extension of Gerstenhaber's theorem fails are also pointed out.
reviewed by: David Ssevviiri
Mathematics Subject Classification ID: 13E15
Mathematics Subject Classification ID: 15A27
Mathematics Subject Classification ID: 13E10
Mathematics Subject Classification ID: 15-04
Mathematics Subject Classification ID: 15A21
zbMATH DE Number: 6371077
zbMATH Keywords: commutative matrix algebras
zbMATH Keywords: irreducible matrix varieties
MaRDI profile type: Publication
full work available at URL: j.laa.2014.10.009
OpenAlex ID: W1967643139
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DOI: 10.1016/J.LAA.2014.10.009
description: scientific article; zbMATH DE number 6371077