Lie triple derivations of unital algebras with idempotents

Benkovič, Dominik

doi:10.1080/03081087.2013.851200

Cited by 61 publications

(27 citation statements)

References 23 publications

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“…Benkovic determined the Lie triple derivations on triangular matrices [4]. More recently, Benkovic described the Lie derivations and Lie triple derivations of upper triangular matrix algebras over a unital algebra [5]. Some other results on the derivations of certain matrix Lie algebras are given in refs.…”

Section: For Any X∈g the Linear Map Ad X Defined By Ad X(y)≔[xy] Fomentioning

confidence: 99%

Lie Triple Derivations of the Lie Algebra of Strictly Block Upper Triangular Matrices

Ghimire¹

2017

J Generalized Lie Theory Appl

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Section: For Any X∈g the Linear Map Ad X Defined By Ad X(y)≔[xy] Fomentioning

confidence: 99%

Lie Triple Derivations of the Lie Algebra of Strictly Block Upper Triangular Matrices

Ghimire¹

2017

J Generalized Lie Theory Appl

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“…It was Krylov who initiated the study of linear mappings on generalized matrix algebras from the point of classifying view [47]. Since then many articles are devoted to this topic, and a number of interesting results are obtained (see [12,15,37,38,52,53,54,67,74,75]). Nevertheless, it leaves so much to be desired.…”

Section: Generalized Matrix Algebras and Examplesmentioning

confidence: 99%

Centralizing traces and Lie triple isomorphisms on generalized matrix algebras

Liang

Wei

Xiao

et al. 2014

Linear and Multilinear Algebra

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Abstract. Let G be a generalized matrix algebra over a commutative ring R and Z(G) be the center of G. Suppose that q : G × G −→ G is an R-bilinear mapping and Tq : G −→ G is the trace of q. We describe the form of Tq satisfying the condition [Tq(G), G] ∈ Z(G) for all G ∈ G. The question of when Tq has the proper form is considered. Using the aforementioned trace function, we establish sufficient conditions for each Lie triple isomorphism of G to be almost standard. As applications we characterize Lie triple isomorphisms of full matrix algebras, of triangular algebras and of certain unital algebras with nontrivial idempotents. Some topics for future research closely related to our current work are proposed at the end of this article.

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“…Cheung [4] initiated the study of various mappings on triangular algebras; in particular, he studied the Lie derivation property for triangular algebras in [3]. Following his work [3], Lie derivations on a wide variety of algebras have been studied by many authors (see [1,2,5,6,7,8,10,11,13,14] and the references therein). The main result of Cheung [3] has recently extended by Du and Wang [5] for a generalized matrix algebra.…”

Section: Introductionmentioning

confidence: 99%

More on Lie derivations of a generalized matrix algebra

Mokhtari¹,

Vishki²

2018

MMN

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Motivated by the Cheung's elaborate work [Linear Multilinear Algebra, 51 (2003), 299-310], we investigate the construction of a Lie derivation on a generalized matrix algebra and apply it to give a characterization for such a Lie derivation to be proper. Our approach not only provides a direct proof for some known results in the theory, but also it presents several sufficient conditions assuring the properness of Lie derivations on certain generalized matrix algebras.

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Lie triple derivations of unital algebras with idempotents

Cited by 61 publications

References 23 publications

Lie Triple Derivations of the Lie Algebra of Strictly Block Upper Triangular Matrices

Lie Triple Derivations of the Lie Algebra of Strictly Block Upper Triangular Matrices

Centralizing traces and Lie triple isomorphisms on generalized matrix algebras

More on Lie derivations of a generalized matrix algebra

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