Representations and cohomologies of modified $ \lambda $-differential Hom-Lie algebras

Yunpeng Xiao; Wen Teng; Yunpeng Xiao; Wen Teng

doi:10.3934/math.2024213

AIMS Mathematics

2024, Volume 9, Issue 2: 4309-4325. doi: 10.3934/math.2024213

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Research article

Representations and cohomologies of modified $ \lambda $-differential Hom-Lie algebras

Yunpeng Xiao ¹,
Wen Teng ^{2
,
,}

1.
School of Mathematical Sciences, Guizhou Normal University, Guiyang 550025, China
2.
School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550025, China

Received: 08 December 2023 Revised: 09 January 2024 Accepted: 10 January 2024 Published: 16 January 2024
MSC : 17A30, 17B10, 17B56, 17B61

In this paper, we introduce the concept and representations of modified $ \lambda $-differential Hom-Lie algebras. We then develop the cohomology of modified $ \lambda $-differential Hom-Lie algebras with coefficients in a suitable representation. As applications, abelian extensions and skeletal modified $ \lambda $-differential Hom-Lie 2-algebras are characterized in terms of cohomology groups.
- Hom-Lie algebras,
- modified $ \lambda $-differential operator,
- cohomology,
- extension,
- Hom-Lie 2-algebras
Citation: Yunpeng Xiao, Wen Teng. Representations and cohomologies of modified $ \lambda $-differential Hom-Lie algebras[J]. AIMS Mathematics, 2024, 9(2): 4309-4325. doi: 10.3934/math.2024213

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Abstract

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

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