Multiplicative Lie n -derivations of generalized matrix algebras

Lie n superderivations and generalized Lie n superderivations of superalgebras

“…By the de nition of generalized Lie triple superderivations, we assume that θ m is a generalized Lie triple superderivation of degree m and β m is a Lie triple superderivation of degree m, m ∈ { , }. According to (5) …”

“…Lie n-derivations were introduced by Abdullaev [3], where the form of Lie n-derivations of a certain von Neumann algebra was described. In 2012, Benkovič and Eremita [4] gave the form of Lie nderivations on triangular rings, which has been generalized to generalized matrix algebras in [5].…”

Centralizing traces and Lie triple isomorphisms on triangular algebras

“…The distinguished feature of our systematic work is that we deal all questions related to (non-)linear mappings of triangular algebras and full matrix algebras under a unified frame, which is the admired generalized matrix algebras frame, see [25,29,30,47,49,50].…”

Characterizations of Lie n-derivations of unital algebras with nontrivial idempotents

“…Many papers discuss mappings on generalized matrix algebras such as [9,10,12,13,17,21,22]. With a quite common assumption that the bimodule A M B is faithful which means that aM = 0 implies a = 0 for each a ∈ A and that M b = 0 implies b = 0 for each b ∈ B, the authors [17,21] obtain sufficient conditions for Lie derivations and Lie n-derivations on generalized matrix algebras to be standard. In this paper, we consider a milder assumption which arises from [2] that the Pierce decomposition (1.1) satisfies exe · eAf = {0} = f Ae · exe implies exe = 0 and eAf · f xf = {0} = f xf · f Ae implies f xf = 0 (1.2) for each x in A.…”