The minimal dimension of maximal commutative subalgebras of full matrix algebras

DOI10.1016/0024-3795(85)90247-2zbMath0578.15008OpenAlexW2061484731WikidataQ127015270 ScholiaQ127015270MaRDI QIDQ1066233

Thomas J. Laffey

Publication date: 1985

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0024-3795(85)90247-2

zbMATH Keywords

matrix algebrafull matrix algebraminimal dimensionmaximal commutative matrix algebraradical of

Mathematics Subject Classification ID

Endomorphism rings; matrix rings (16S50) Finite rings and finite-dimensional associative algebras (16P10) Algebraic systems of matrices (15A30)

Related Items (22)

Algorithm to compute the maximal Abelian dimension of Lie algebras ⋮ Maximal Commutative Subalgebras ofn×nMatrices ⋮ The length function and matrix algebras ⋮ Two-generated commutative matrix subalgebras ⋮ Abelian tensors ⋮ Commutative nilpotent subalgebras with nilpotency index \(n-1\) in the algebra of matrices of order \(n\) ⋮ Classification of matrix subalgebras of length 1. ⋮ Cauchy problems related to integrable matrix hierarchies ⋮ Modules and matrices ⋮ Algorithmic method to obtain abelian subalgebras and ideals in Lie algebras ⋮ Maximal abelian subalgebras of pseudoorthogonal Lie algebras ⋮ On the symplectic structures in frame bundles and the finite dimension of basic symplectic cohomologies ⋮ On the maximal, commutative, subalgebras of 14 by 14 matrices ⋮ Constructing Maximal Commutative Subalgebras of Matrix Rings in Small Dimensions ⋮ Commutative matrix subalgebras and length function ⋮ Maximal abelian subalgebras of pseudounitary Lie algebras ⋮ Maximal abelian subalgebras of complex orthogonal Lie algebras ⋮ Maximal abelian subalgebras of \(e(p,q)\) algebras ⋮ Maximal subalgebras of finite-dimensional algebras ⋮ Some aspects of Olga Taussky's work in algebra ⋮ Abelian subalgebras on Lie algebras ⋮ Maximal commutative subalgebras of matrix algebras

Cites Work

• On maximal commutative algebras of linear transformations
• The dimension of maximal commutative subalgebras of \(K_ n\)
• On dominance and varieties of commuting matrices
• Maximal commutative subalgebras of K\(_n\) at exponent three
• Maximal abelian subalgebras of real and complex symplectic Lie algebras
• Endliche Gruppen I
• Unnamed Item

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