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Research Article | Open Access

The full cohomology, abelian extensions and formal deformations of Hom-pre-Lie algebras

Shanshan Liu1, Abdenacer Makhlouf2( ), Lina Song3
Department of Mathematics, Zhejiang University of Science and Technology, Hangzhou 310023, China
University of Haute Alsace, IRIMAS-Mathematics department, Mulhouse, France
Department of Mathematics, Jilin University, Changchun 130012, Jilin, China
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Abstract

The main purpose of this paper is to provide a full cohomology of a Hom-pre-Lie algebra with coefficients in a given representation. This new type of cohomology exploits strongly the Hom-type structure and fits perfectly with simultaneous deformations of the multiplication and the homomorphism defining a Hom-pre-Lie algebra. Moreover, we show that its second cohomology group classifies abelian extensions of a Hom-pre-Lie algebra by a representation.

Keywords

Hom-pre-Lie algebracohomologyabelian extensionformal deformation

References

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Electronic Research Archive
Volume 30 Issue 8,
August 2022
Pages 2748-2773
DOI: 10.3934/era.2022141

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Cite this article:
Liu S, Makhlouf A, Song L. The full cohomology, abelian extensions and formal deformations of Hom-pre-Lie algebras. Electronic Research Archive, 2022, 30(8): 2748-2773. https://doi.org/10.3934/era.2022141

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Received: 18 September 2021
Revised: 10 March 2022
Accepted: 12 March 2022
Published: 15 August 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)