Cohomology and automorphisms of Com-PreLie algebras
Tao Zhang, Ying-Hua Lu
TL;DR
This paper develops cohomology theories for Com-PreLie algebras, investigates abelian extensions, and establishes conditions for automorphism inducibility using Wells sequences.
Contribution
It introduces cohomology for Com-PreLie algebras and analyzes automorphism inducibility within this framework, a novel approach in the field.
Findings
Cohomology groups applied to abelian extensions
Necessary and sufficient conditions for automorphism inducibility
Use of Wells exact sequences to study automorphisms
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.
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