Biderivations and linear commuting maps on the Lie algebra

Cheng, Xiaosheng; Wang, Minjing; Sun, Jiancai; Zhang, Honglian

doi:10.1080/03081087.2016.1277688

Cited by 33 publications

(7 citation statements)

References 6 publications

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“…A mapping φ of a Lie algebra g is called commuting if [φ(x), x] = 0 for any x in g (see [2]). An important application of linear commuting mappings is to construct biderivations (for example, see [2,6,20,21]), as shown in the following lemma. Lemma 1.2.…”

Section: Introductionmentioning

confidence: 99%

Biderivations and linear commuting mappings of $\mathbb{N}$-graded Lie algebras of maximal class

Yang¹,

Tang²,

Chen³

2021

Preprint

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Combined with Fialowski's classification for algebras of maximal class and using the first cohomology of these Lie algebras with coefficients in the adjoint module, in this paper we determine the skew-symmetric biderivation spaces for all algebras of maximal class with 1-dimensional homogeneous components m 0 , L 1 and m 2 as the given gradings, up to isomorphism. Different from the usual conclusions, we obtain that a non-simple Lie algebra L 1 only has inner biderivations. As an application, we characterize linear commuting mappings on these algebras.

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Section: Introductionmentioning

confidence: 99%

Biderivations and linear commuting mappings of $\mathbb{N}$-graded Lie algebras of maximal class

Yang¹,

Tang²,

Chen³

2021

Preprint

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“…Recall that a map ϕ : A → A is called an additive (a linear) commuting if ϕ is additive (linear) and [ϕ(a), a] = 0 for all a ∈ A. The problem of characterizing additive or linear commuting maps on various rings and algebras had been studied (for example, see [2,3,6,7,11] and the references therein). The readers can also see a survey paper [4] about commuting maps.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear anti-commuting maps of unital algebras with idempotents

Feng¹,

Qi²

2019

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“…The biderivations of Lie algebras have been sufficiently studied. In [2,3,15], the authors proved that all anti-symmetric biderivations on the Schrödinger-Virasoro algebra, the simple generalized Witt algebra and the infinite-dimensional Galilean conformal algebra are inner, respectively. In [7], the authors determined all the skewsymmetric biderivations of W(a;b) and found that there exist non-inner biderivations.…”

Section: Introductionmentioning

confidence: 99%