Results 1 to 10 of about 166 (161)
Nonlinear Lie Triple Higher Derivations on Triangular Algebras by Local Actions: A New Perspective
Axioms, 2022 Let R be a commutative ring with unity and T be a triangular algebra over R. Let a sequence Δ={δn}n∈N of nonlinear mappings δn:T→T is a Lie triple higher derivation by local actions satisfying the equation.
Xinfeng Liang, Dandan Ren, Qingliu Li
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Characterization of Lie-Type Higher Derivations of von Neumann Algebras with Local Actions
Mathematics, 2023 Let m and n be fixed positive integers. Suppose that A is a von Neumann algebra with no central summands of type I1, and Lm:A→A is a Lie-type higher derivation.
Ab Hamid Kawa +4 more
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Lie algebras of vertical derivations on semiaffine varieties with torus actions [PDF]
Journal of Pure and Applied Algebra, 2021 Let X be a normal variety endowed with an algebraic torus action. An additive group action $α$ on X is called vertical if a general orbit of $α$ is contained in the closure of an orbit of the torus action and the image of the torus normalizes the image of $α$ in Aut(X).
Arzhantsev, Ivan +2 more
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Triangular algebras with nonlinear higher Lie n-derivation by local actions
AIMS Mathematics, 2023 <abstract><p>This paper was devoted to the study of the so-called nonlinear higher Lie n-derivation of triangular algebras $ \mathcal{T} $, where $ n $ is a nonnegative integer greater than two. Under some mild conditions, we proved that every nonlinear higher Lie n-derivation by local actions on the triangular algebras is of a standard ...
Xinfeng Liang, Mengya Zhang
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Linear maps on von Neumann algebras acting as Lie type derivation via local actions
AIMS Mathematics, 2021 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mohd Arif Raza +3 more
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Lie Derivations on Generalized Matrix Algebras by Local Actions
AxiomsLet G=G(A,B,M,N) be a generalized matrix algebra. A linear map Δ:G→G is called a Lie derivation at E∈G if Δ([U,V])=[Δ(U),V]+[U,Δ(V)] for all pairs U,V∈G such that UV=E. In this paper, we use techniques of matrix decomposition and algebraic identity analysis to fully characterize the general form of Lie derivations at E=e0000, where e0 is an arbitrary ...
Jinhong Zhuang, Yanping Chen, Yijia Tan
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Characterizing Lie derivations on triangular algebras by local actions
The Electronic Journal of Linear Algebra, 2013 Let U = Tri(A,M,B) be a triangular algebra, where A, B are unital algebras over a field F and M is a faithful (A,B)-bimodule. Assume that 2 F and L : U ! U is a map. It is shown that, under some mild conditions, L is linear and satisfies L((X,Y )) = (L(X),Y ) + (X,L(Y )) for any X,Y 2 U with (X,Y ) = XY − Y X = 0 if and only if L(X) = '(X) + ZX + f(X)
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Nonlinear Mixed Lie Triple Derivations by Local Actions on Von Neumann Algebras
Journal of Mathematical StudySummary: As a generalization of global mappings, we study a class of non-global mappings in this note. Let \(\mathcal{A} \subseteq B (\mathcal{H})\) be a von Neumann algebra without abelian direct summands. We prove that if a map \(\delta : \mathcal{A} \rightarrow \mathcal{A}\) satisfies \(\delta ([[A,B]_\ast ,C]) = [[ \delta (A),B]_\ast ,C]+ [[A ...
Gao, Meilian, Zhao, Xingpeng
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FilomatLet U be a triangular operator algebra, and ?: U ? U be a linear map. In this paper, under some mild conditions on U, we prove that if ? satisfies ?([[U, V], W ]) = [[?(U), V], W ] = [[U, ?(V)], W] for any U, V, W ? U with UV = UW = P being the standard idempotent(resp. UV = UW = 0), then there exist ? ? Z(U) and a linear map ?: U ? Z(U) satisfying ?([[
Xinzhuo Liu, Jianhua Zhang
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Derivations and KMS-Symmetric Quantum Markov Semigroups. [PDF]
Commun Math Phys, 2023 Vernooij M, Wirth M.
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