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arXiv · 2510.23611

Cohomology and automorphisms of Com-PreLie algebras

Tao Zhang·Ying-Hua Lu
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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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Tao Zhang, Ying-Hua Lu. 2025-09-30. Cohomology and automorphisms of Com-PreLie algebras. https://arxiv.org/abs/2510.23611

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