Cohomology and automorphisms of Com-PreLie algebras

2025/09/30 by Zhang, Tao, Lu, Ying-Hua
#FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2510.23611

Abstract

This paper introduces the concept of representations for Com-PreLie algebras and develops corresponding cohomology theories, examining how cohomology groups can be applied in the context of Com-PreLie algebras. Initially, we utilize the cohomology theory to investigate abelian extensions of Com-PreLie algebras. Next, given an abelian extension of Com-PreLie algebras and its representation, we explore the inducibility of Com-PreLie automorphisms, deriving both necessary and sufficient conditions for the inducibility problem. Lastly, we delve deeper into the inducibility of Com-PreLie automorphisms using the Wells exact sequences, offering a clear framework for studying the inducibility of Com-PreLie automorphisms.

Citations

• Applications of Poisson cohomology to the inducibility problems and study of deformation maps
• Deformations and abelian extensions of compatible pre-Lie algebras
• Non-abelian extensions of Rota-Baxter Lie algebras and inducibility of automorphisms
• Cofree Com-PreLie algebras
• A prelie algebra associated to a linear endomorphism and related algebraic structures
• The Hopf algebra of Fliess operators and its dual pre-Lie algebra
• Cohomologies and deformations of right-symmetric algebras

Related

• Cofree Com-PreLie algebras
• Examples of Com-PreLie Hopf algebras
• Cocommutative Com-PreLie bialgebras
• Cohomology and automorphisms for a matched pair of 3-Lie algebras
• Non-abelian extensions and Wells exact sequences of Bol algebras