Biderivations of triangular algebras

Benkovič, Dominik

doi:10.1016/j.laa.2009.05.029

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2012

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Cited by 79 publications

(39 citation statements)

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“…He described automorphisms, derivations, commuting mappings and Lie derivations of triangular algebras in [4,5,6]. Benkovič [1] studied biderivations of triangular algebras and showed that under certain conditions every biderivation on a triangular algebra is the sum of an extremal biderivation and an inner biderivation. Zhang and Yu [16] proved that any Jordan derivation on a triangular algebra is a derivation.…”

Section: A M B )mentioning

confidence: 99%

Characterizations of Lie Higher and Lie Triple Derivations on Triangular Algebras

Li¹,

Shen²

2012

Journal of the Korean Mathematical Society

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Section: A M B )mentioning

confidence: 99%

Characterizations of Lie Higher and Lie Triple Derivations on Triangular Algebras

Li¹,

Shen²

2012

Journal of the Korean Mathematical Society

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“…In recent years, biderivations have aroused the interest of a great many authors, see [2,5,8,9,12,13,16,17,18,19]. In [2], Brešar et.…”

Section: Introduction and Preliminary Resultsmentioning

confidence: 99%

Biderivations of finite-dimensional complex simple Lie algebras

Tang

2017

Linear and Multilinear Algebra

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Abstract. In this paper, we prove that a biderivation of a finite dimensional complex simple Lie algebra without the restriction of skewsymmetric is inner. As an application, the biderivation of a general linear Lie algebra is presented. In particular, we find a class of a non-inner and non-skewsymmetric biderivations. Furthermore, we also get the forms of linear commuting maps on the finite dimensional complex simple Lie algebra or general linear Lie algebra.

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“…Benkovič and Eremita [2] studied commuting traces of bilinear maps and Lie isomorphisms of triangular algebras. Benkovič [3] investigated biderivations of triangular algebras. Wong [19] treated Jordan isomorphisms of triangular algebras, while Zhang and Yu [20,21] studied Jordan derivations and nonlinear Lie derivations.…”

Section: Introductionmentioning

confidence: 99%