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Research Article | Open Access

Representations and cohomologies of modified λ-differential Hom-Lie algebras

Yunpeng Xiao1, Wen Teng2( )
School of Mathematical Sciences, Guizhou Normal University, Guiyang 550025, China
School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550025, China
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Abstract

In this paper, we introduce the concept and representations of modified λ-differential Hom-Lie algebras. We then develop the cohomology of modified λ-differential Hom-Lie algebras with coefficients in a suitable representation. As applications, abelian extensions and skeletal modified λ-differential Hom-Lie 2-algebras are characterized in terms of cohomology groups.

Keywords

Hom-Lie algebrasmodified λ-differential operatorcohomologyextensionHom-Lie 2-algebras
CLC number: 17A30, 17B10, 17B56, 17B61

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AIMS Mathematics
Volume 9 Issue 2,
February 2024
Pages 4309-4325
DOI: 10.3934/math.2024213

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Cite this article:
Xiao Y, Teng W. Representations and cohomologies of modified λ-differential Hom-Lie algebras. AIMS Mathematics, 2024, 9(2): 4309-4325. https://doi.org/10.3934/math.2024213

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Received: 08 December 2023
Revised: 09 January 2024
Accepted: 10 January 2024
Published: 15 February 2024
©2024 the Author(s), licensee AIMS Press.

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