Lie (Jordan) centralizers on generalized matrix algebras

Characterizations of Lie n -Centralizers on Certain Trivial Extension Algebras

“…We claim that τ(U ∝ M)⊆Z(U ∝ M). Indeed, according to (6), it sufces to prove that [τ U (u), m] � 0 for all u ∈ U, m ∈ M. Since f U − τ U is a centralizer and f U is a Lie n-centralizer, it follows from the assumption (1)(ii) and Lemma 2 that…”

“…Ten, the R-linear map δ: U ⟶ U is called a proper Lie centralizer. Recently, the structure of Lie centralizers is studied by many mathematicians (see [6][7][8][9][10]).…”

Lie centralizers and commutant preserving maps on generalized matrix algebras

“…Also, in [30] non-linear Lie centralizers on generalized matrix algebra have been characterized. In [25] it has been shown that under some conditions on a unital generalized matrix algebra G, if φ : G → G is a linear Lie centralizer, then φ(a) = λa + µ(a) in which λ ∈ Z(G) and µ is a linear map from G into Z(G) vanishing at commutators. Ghimire [20] has investigated the linear Lie centralizers of the algebra of dominant block upper triangular matrices.…”

Lie triple maps on generalized matrix algebras

“…In [6], Fošner and Jing have described the non-additive Lie centralizers on triangular algebras. Jabeen in [9] has described Lie centralizers on generalized matrix algebras, and in [12] non-linear Lie centralizers on generalized matrix algebra have been studied. In [1], the authors have studied the characterization of Lie centralizers on non-unital triangular algebras through zero products, and in [8] Lie centralizers at zero products on a class of operator algebras have been characterized.…”