Results 1 to 10 of about 194 (182)
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
doaj +5 more sources
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
doaj +5 more sources
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)
Xiaofei Qi, Qi, Xiaofei
openaire +2 more sources
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
openaire +2 more sources
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
openaire +3 more sources
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
openaire +2 more sources
Representations and actions of Hopf algebras [PDF]
, 2021 The larger area of my thesis is Algebra; more specifically, my work belongs to the following two major branches of Algebra: \emph{representation theory} and \emph{invariant theory}.
Yammine, Ramy
core +1 more source
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
openaire +3 more sources
Crystallographic actions on Lie groups and post-Lie algebra structures [PDF]
, 2021 summary:This survey on crystallographic groups, geometric structures on Lie groups and associated algebraic structures is based on a lecture given in the Ostrava research seminar in $2017$
Burde, Dietrich
core +1 more source
Algebras with representable representations
, 2021 Just like group actions are represented by group automorphisms, Lie algebra actions are represented by derivations: up to isomorphism, a split extension of a Lie algebra $B$ by a Lie algebra~$X$ corresponds to a Lie algebra morphism $B\to \mathrm{Der}(X)$
Van der Linden, Tim +1 more
core +2 more sources