Jordan derivations and antiderivations of generalized matrix algebras

Li, Yanbo; Wyk, Leon van; Wei, Feng

doi:10.7153/oam-07-23

Cited by 28 publications

(38 citation statements)

References 17 publications

(35 reference statements)

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“…It is worth pointing out that the notion of generalized matrix algebras efficiently unifies triangular algebras with full matrix algebras. The distinguished feature of our systematic work is that we deal with all questions related to additive mappings of triangular algebras and full matrix algebras under a unified frame, which is the admired generalized matrix algebras frame (see [8,12,13,16]). …”

Section: Preliminariesmentioning

confidence: 99%

Zero triple product determined generalized matrix algebras

Han¹

2015

Turk J Math

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Section: Preliminariesmentioning

confidence: 99%

Zero triple product determined generalized matrix algebras

Han¹

2015

Turk J Math

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“…Let M n (R) be the full matrix algebra consisting of all n × n matrices over R. It is worth to point out that the notion of generalized matrix algebras efficiently unifies triangular algebras with full matrix algebras together. The feature of our systematic work is to deal with all questions related to (non-)linear mappings of triangular algebras and of full matrix algebras under a unified frame, which is the admired generalized matrix algebras frame, see [41,52,53,54,74,75]. Let us list some classical examples of generalized matrix algebras which will be revisited in the sequel (Section 3 and Section 4).…”

Section: Generalized Matrix Algebras and Examplesmentioning

confidence: 99%

“…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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“…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].…”

Section: Topics For Further Researchmentioning

confidence: 99%

Centralizing traces and Lie triple isomorphisms on triangular algebras

Xiao

Wei

Fošner

2014

Linear and Multilinear Algebra

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

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Jordan derivations and antiderivations of generalized matrix algebras

Cited by 28 publications

References 17 publications

Zero triple product determined generalized matrix algebras

Zero triple product determined generalized matrix algebras

Centralizing traces and Lie triple isomorphisms on generalized matrix algebras

Centralizing traces and Lie triple isomorphisms on triangular algebras

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