An Operadic Generalization of the Gerstenhaber-Shack Theorem
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866910782227218432 |
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| author | Yu, Andy |
| author_facet | Yu, Andy |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_07519 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An Operadic Generalization of the Gerstenhaber-Shack Theorem Yu, Andy Algebraic Topology Algebraic Geometry 18N70, 16S80 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. |
| title | An Operadic Generalization of the Gerstenhaber-Shack Theorem |
| topic | Algebraic Topology Algebraic Geometry 18N70, 16S80 |
| url | https://arxiv.org/abs/2501.07519 |