The maximum dimension of a Lie nilpotent subalgebra of $\boldsymbol {\mathbb {M}_n(F)}$ of index $\boldsymbol {m}$

DOI10.1090/tran/7821zbMath1456.16027arXiv1608.04562OpenAlexW2964194331MaRDI QIDQ5234498

Michał Ziembowski, Jenő Szigeti, Leon van Wyk, Jacob Van Den Berg

Publication date: 26 September 2019

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1608.04562

zbMATH Keywords

matrix algebraLie algebradimensionLie nilpotentcommutative subalgebra

Mathematics Subject Classification ID

Endomorphism rings; matrix rings (16S50) Generalizations of commutativity (associative rings and algebras) (16U80) Lie algebras and Lie superalgebras (17B99) Identities other than those of matrices over commutative rings (16R40)

Related Items (6)

Construction of a class of maximal commutative subalgebras of prime Leavitt path algebras ⋮ Lie properties in associative algebras ⋮ Lie solvability and the identity \([x_{1},y_{1}[x_{2},y_{2}]\cdots[x_{q},y_{q}]=0\) in certain matrix algebras] ⋮ The maximal abelian dimension of a Lie algebra, Rentschler's property and Milovanov's conjecture ⋮ Maximal commutative subalgebras of Leavitt path algebras ⋮ Lengths of cyclic algebras and commutative subalgebras of quaternion matrices

Cites Work

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• On maximal commutative algebras of linear transformations
• Cayley-Hamilton theorem for \(2\times 2\) matrices over the Grassmann algebra
• On the dimension of faithful modules over finite dimensional basic algebras
• Polynomial identity rings.
• Simultaneous triangularization
• On Lie Nilpotent Rings and Cohen's Theorem
• Schur's inequality for the dimension of commuting families of matrices
• A Simple Proof of a Theorem of Schur
• Associative rings satisfying the Engel condition
• New determinants and the Cayley-Hamilton Theorem for matrices over Lie nilpotent rings
• A Short Note on the Schur-Jacobson Theorem
• Schur’s theorems on commutative matrices

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