@article{Liu2022, 
author = {Shanshan Liu and Abdenacer Makhlouf and Lina Song},
title = {The full cohomology, abelian extensions and formal deformations of Hom-pre-Lie algebras},
year = {2022},
journal = {Electronic Research Archive},
volume = {30},
number = {8},
pages = {2748-2773},
keywords = {cohomology, abelian extension, Hom-pre-Lie algebra, formal deformation},
url = {https://www.sciopen.com/article/10.3934/era.2022141},
doi = {10.3934/era.2022141},
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.}
}