An Operadic Generalization of the Gerstenhaber-Shack Theorem

Andy Yu

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arXiv · 2501.07519

An Operadic Generalization of the Gerstenhaber-Shack Theorem

Andy Yu

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Abstract

A simplicial cochain complex can be derived from a locally small poset by taking the nerve of the poset viewed as a category. We show that the simplicial cochain complex and a relative Hochschild cochain complex of the incidence algebra of the poset are isomorphic as operads with multiplications. This result implies that the hG-algebras derived from those operads are isomorphic, which is a generalization of the Gerstenhaber-Shack theorem. The isomorphism also induces a differential graded Lie algebra isomorphism, which we use to compute the moduli space of formal deformations of the incidence algebra.

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BibTeX RIS

Andy Yu. 2025-01-13. An Operadic Generalization of the Gerstenhaber-Shack Theorem. https://arxiv.org/abs/2501.07519

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