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December, 2018 Biderivations and Commutative Post-Lie Algebra Structures on the Lie Algebra $\mathcal{W}(a,b)$
Xiaomin Tang
Taiwanese J. Math. 22(6): 1347-1366 (December, 2018). DOI: 10.11650/tjm/180305

Abstract

For $a,b \in \mathbb{C}$, the Lie algebra $\mathcal{W}(a,b)$ is the semidirect product of the Witt algebra and a module of the intermediate series. In this paper, all biderivations of $\mathcal{W}(a,b)$ are determined. Surprisingly, these Lie algebras have symmetric (and skew-symmetric) non-inner biderivations. As an application, commutative post-Lie algebra structures on $\mathcal{W}(a,b)$ are obtained.

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Xiaomin Tang. "Biderivations and Commutative Post-Lie Algebra Structures on the Lie Algebra $\mathcal{W}(a,b)$." Taiwanese J. Math. 22 (6) 1347 - 1366, December, 2018. https://doi.org/10.11650/tjm/180305

Information

Received: 29 October 2017; Revised: 23 February 2018; Accepted: 30 March 2018; Published: December, 2018
First available in Project Euclid: 18 April 2018

zbMATH: 07021693
MathSciNet: MR3878572
Digital Object Identifier: 10.11650/tjm/180305

Subjects:
Primary: 17B05 , 17B40 , 17B68

Keywords: biderivation , Lie algebra $\mathcal{W}(a,b)$ , post-Lie algebra

Rights: Copyright © 2018 The Mathematical Society of the Republic of China

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Vol.22 • No. 6 • December, 2018
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