On maps preserving Lie products equal to a rank-one nilpotent

DOI10.1016/j.laa.2020.02.007zbMath1445.15013OpenAlexW3004808574WikidataQ115344264 ScholiaQ115344264MaRDI QIDQ2310398

Hayden Julius, Victor Ginzburg, Ricardo Velasquez

Publication date: 6 April 2020

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

Full work available at URL: https://doi.org/10.1016/j.laa.2020.02.007

zbMATH Keywords

linear preserverscommutativity preserving mapsrank-one nilpotency

Mathematics Subject Classification ID

Commutativity of matrices (15A27) Linear transformations, semilinear transformations (15A04) Linear preserver problems (15A86)

Related Items (8)

On maps preserving products equal to fixed elements ⋮ Fixed product preserving mappings on Banach algebras ⋮ Nonlinear maps preserving certain subspaces of Lie product of operators ⋮ On maps preserving Lie products equal to e₁₁ - e₂₂ ⋮ Linear maps preserving products equal to primitive idempotents of an incidence algebra ⋮ On maps preserving rank-one nilpotents ⋮ On maps preserving products equal to a diagonalizable matrix ⋮ On maps preserving square roots of idempotent and rank-one nilpotent matrices

Cites Work

• On bilinear maps on matrices with applications to commutativity preservers.
• Commutativity preserving maps
• On operators preserving commutativity
• Linear maps that preserve commuting pairs of matrices
• On maps preserving products of matrices
• Pairs of matrices, one of which commutes with their commutator
• A note on pairs of matrices with rank one commutator
• Commuting Traces of Biadditive Mappings, Commutativity-Preserving Mappings and Lie Mappings
• Simultaneous triangularization of matrices—low rank cases and the nonderogatory case
• On maps preserving rank-one nilpotents

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