Commutativity preserving linear maps on central simple algebras.

DOI10.1016/j.jalgebra.2004.09.014zbMath1072.16028OpenAlexW2029771737MaRDI QIDQ1764832

Matej Brešar, Peter Šemrl

Publication date: 22 February 2005

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2004.09.014

zbMATH Keywords

central simple algebrascommutativity-preserving maps

Mathematics Subject Classification ID

Finite rings and finite-dimensional associative algebras (16P10) Automorphisms and endomorphisms (16W20) Linear transformations, semilinear transformations (15A04)

Related Items (23)

Maps on matrix spaces ⋮ Biderivations and strong commutativity-preserving maps on parabolic subalgebras of simple Lie algebras ⋮ Nonlinear Strong Commutativity Preserving Maps on Prime Rings ⋮ On bilinear maps on matrices with applications to commutativity preservers. ⋮ Strong commutativity preserving maps on von Neumann algebras ⋮ Nonlinear strong commutativity preserving maps on skew elements of prime rings with involution. ⋮ Strong commutativity preserving generalized derivations on right ideals. ⋮ Nonlinear maps preserving Lie products on triangular algebras ⋮ A note on strong skew Jordan product preserving maps on von Neumann algebras ⋮ Strong commutativity preserving maps on rings. ⋮ Commutativity preserving maps revisited. ⋮ Nonlinear maps preserving Lie products on factor von Neumann algebras ⋮ Strong commutativity preserving maps on Lie ideals. ⋮ Maps preserving square-zero matrices on the algebra consisting of all upper triangular matrices ⋮ Linear maps on matrices preserving commutativity up to a factor ⋮ Strong (skew) ξ-Lie commutativity preserving maps on algebras ⋮ Strong commutativity preserving generalized derivations on Lie ideals ⋮ Strong commutativity preserving maps of strictly triangular matrix Lie algebras ⋮ Strong commutativity preserving derivations on Lie ideals of prime Γ-rings ⋮ Strong commutativity preserving maps in prime rings with involution. ⋮ On maps preserving zeros of the polynomial \(xy - yx^\ast\) ⋮ Unnamed Item ⋮ A characterization of additive derivations on $C^*$-algebras

Cites Work

• Unnamed Item
• Linear maps that preserve commuting pairs of matrices
• Commuting maps: a survey.
• Commuting Traces of Biadditive Mappings, Commutativity-Preserving Mappings and Lie Mappings
• Centralizers in Free Associative Algebras
• Preserving commutativity

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