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Research Article | Open Access

Abelian extensions of Lie triple systems with derivations

Xueru Wu, Yao Ma, Liangyun Chen( )
School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China
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Abstract

Let L and A be Lie triple systems, and let θA be a representation of L on A. We first construct the third-order cohomology classes by derivations of A and L, then obtain a Lie algebra GθA with a representation Φ on H3(L,A), where θA is given by an abelian extension

0⟶A⟶L~→πL⟶0.

We study obstruction classes for extensibility of derivations of A and L to those of L~. An application of Φ is discussed.

Keywords

Lie triple systemcohomologyderivationabelian extension

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Electronic Research Archive
Volume 30 Issue 3,
March 2022
Pages 1087-1103
DOI: 10.3934/era.2022058

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Cite this article:
Wu X, Ma Y, Chen L. Abelian extensions of Lie triple systems with derivations. Electronic Research Archive, 2022, 30(3): 1087-1103. https://doi.org/10.3934/era.2022058

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Received: 22 July 2021
Revised: 29 November 2021
Accepted: 06 December 2021
Published: 15 March 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)