The minimal dimension of maximal commutative subalgebras of full matrix algebras
type: Item
instance of: scholarly article
title: The minimal dimension of maximal commutative subalgebras of full matrix algebras
zbMATH Open document ID: 0578.15008
DOI: 10.1016/0024-3795(85)90247-2
author: Thomas J. Laffey
published in: Linear Algebra and its Applications
publication date: 1985-01-01T00:00:00Z
review text: A commutative subalgebra A of the full matrix algebra \(M_ n(F)\) over a field F is said to be maximal if the centralizer of A equals A. The purpose of this paper is to determine a lower bound for the dimension of such a subalgebra of \(M_ n(F)\). The author shows that if A is a maximal commutative subalgebra of \(M_ n(F)\) with (rad A)\({}^ 3=0\), then dim \(A\geq [3n^{2/3}-4]\), where rad A is the radical of A and [ ] denotes the greatest-integer function, and that this is the best possible lower bound by giving the explicit construction of an example attaining it for each n. In general case, it is shown that if A is a commutative subalgebra of \(M_ n(F)\), then dim A\(>(2n)^{2/3}-1\).
Mathematics Subject Classification ID: 15A30
Mathematics Subject Classification ID: 16S50
Mathematics Subject Classification ID: 16P10
zbMATH DE Number: 3925006
zbMATH Keywords: minimal dimension
zbMATH Keywords: maximal commutative matrix algebra
zbMATH Keywords: radical of
zbMATH Keywords: matrix algebra
zbMATH Keywords: full matrix algebra
MaRDI profile type: Publication
full work available at URL: 0024-3795(85)90247-2
OpenAlex ID: W2061484731
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Wikidata QID: Q127015270
description: scientific article; zbMATH DE number 3925006