Biderivations and linear commuting maps on simple generalized Witt algebras over a field

By Zhengxin Chen. 2016

82 citations recorded by the source corpus.

Let W be a simple generalized Witt algebras over a field of characteristic zero. In this paper, it is proved that each anti-symmetric biderivation of W is inner. As an application of biderivations, it is shown that a linear map ψ on W is commuting if and only if ψ is a scalar multiplication map on W. The commuting automorphisms and derivations of W are determined.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/cfb85c2befa841e7ede6b8e086c7c6135e68b2cb

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In Algebra and Number Theory

1. Xiaomin Tang
2. Xiansheng Dai
3. Guangzhe Fan

In Geometry and Topology

1. Xiaomin Tang
2. Xiansheng Dai
3. Guangzhe Fan
4. S. Stević

In Mathematical Physics

1. Xiansheng Dai
2. Guangzhe Fan
3. Xiaomin Tang

Citations in the corpus

• Biderivations of finite-dimensional complex simple Lie algebras (2016, methodology): “Chen [3], noted that every skewsymmetric biderivation of a simple generalized Witt algebra over a field of characteristic zero is also an inner biderivation.”
• Super-biderivations of Lie superalgebras (2016, methodology): “We present some modified results of biderivations of Lie algebras in [8] .”
• Biderivations, linear commuting maps and commutative post-Lie algebra structures on W-algebras (2017, background): “About the recent articles on commuting maps we can reference [3, 6, 7, 11, 13, 16, 22, 32, 35, 36].”
• Biderivations and Commuting Linear Maps on Lie Algebras (2018, unknown): “, computing δ([x, y], [z, w]) in two different ways, is well-known; it was first used in associative rings [5], and later also in Lie algebras [6].”