Commutativity preserving linear maps and Lie automorphisms of strictly triangular matrix space

DOI10.1016/S0024-3795(02)00264-1zbMath1007.15007OpenAlexW1989709054WikidataQ115340035 ScholiaQ115340035MaRDI QIDQ1611875

Chong Huang, You'an Cao, Chon Hu Cheng

Publication date: 28 August 2002

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

Full work available at URL: https://doi.org/10.1016/s0024-3795(02)00264-1

zbMATH Keywords

linear mapsmatrix spacecommutativity preservingLie automorphismsstrictly upper triangular matrices

Mathematics Subject Classification ID

Commutativity of matrices (15A27) Hermitian, skew-Hermitian, and related matrices (15B57) Linear transformations, semilinear transformations (15A04)

Related Items (12)

Regular Hom–Lie structures on strictly upper triangular matrix Lie algebras ⋮ The group of commutativity preserving maps on strictly upper triangular matrices ⋮ Invertible linear maps on Borel subalgebras preserving zero Lie products ⋮ Commutativity-preserving maps on Lie ideals of prime algebras. ⋮ Injective strong commutativity preservers on \(\mathcal{T}_{\infty}(F)\) ⋮ Inexact GMRES for singular linear systems ⋮ Maps preserving square-zero matrices on the algebra consisting of all upper triangular matrices ⋮ Nonlinear bijective maps on strictly upper triangular matrices preserving zero product ⋮ Quotient convergence and multi-splitting methods for solving singular linear equations ⋮ Strong commutativity preserving maps of strictly triangular matrix Lie algebras ⋮ Invertible linear maps on simple Lie algebras preserving commutativity ⋮ Unnamed Item

Cites Work

• Commutativity-preserving operators on symmetric matrices
• On operators preserving commutativity
• Linear transformations on symmetric matrices that preserve commutativity
• Linear preserver problems: A brief introduction and some special techniques
• Linear maps that preserve commuting pairs of matrices
• Commutativity preserving linear maps and Lie automorphisms of triangular matrix algebras
• Automorphisms of the Lie algebra of upper triangular matrices over a connected commutative ring
• Automorphisms of certain Lie algebras of upper triangular matrices over a commutative ring
• A note on algebra automorphisms of strictly upper triangular matrices over commutative rings
• Linear maps preserving commutativity
• Automorphisms of certain unipotent groups
• Linear Preserver Problems
• Linear transformations on matrices: The invariance of commuting pairs of matrices
• Invariants of linear maps on matrix algebras
• Commutativity-preserving and normal-preserving linear transformations on
• Automorphisms of the Lie algebra of strictly upper triangular matrices over certain commutative rings

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