2021/11/22 by Shanshan Liu, Liu, Shanshan, Abdenacer Makhlouf +3
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Physical sciences #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph)
paper · pdf · doi:10.48550/arxiv.2111.11015
openalex publication_date 2021/11/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 exploit 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.