$A_{\infty}$-structures on the additive decomposition of the Tate-Hochschild cohomology of a finite group algebra
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arXiv
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| Auteurs principaux: | , , , , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866909979844280320 |
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| author | Bian, Xiuli Li, Longfei Liu, Yuming Wang, Tianyun Wang, Zhengfang Zhou, Guodong |
| author_facet | Bian, Xiuli Li, Longfei Liu, Yuming Wang, Tianyun Wang, Zhengfang Zhou, Guodong |
| contents | Firstly, for a finite group algebra, we provide a computational framework $\widehat{m}_n$ for the Tate-Hochschild cochain complex in terms of the additive decomposition, by decomposing each planar n-ary tree into local two children and local three children. Secondly, we give all $\widehat{m}_2$ formulas of the Tate-Hochschild cochain complex in terms of the additive decomposition. Thirdly, we give explicit $A_{\infty}$-multiplication formulas for both the Hochschild cochain complex and the Hochschild chain complex under additive decompositions. Finally, we give $A_{\infty}$-multiplication formulas in the context of abelian groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_00351 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | $A_{\infty}$-structures on the additive decomposition of the Tate-Hochschild cohomology of a finite group algebra Bian, Xiuli Li, Longfei Liu, Yuming Wang, Tianyun Wang, Zhengfang Zhou, Guodong K-Theory and Homology Rings and Algebras 16E40, 20J06, 18G70, Firstly, for a finite group algebra, we provide a computational framework $\widehat{m}_n$ for the Tate-Hochschild cochain complex in terms of the additive decomposition, by decomposing each planar n-ary tree into local two children and local three children. Secondly, we give all $\widehat{m}_2$ formulas of the Tate-Hochschild cochain complex in terms of the additive decomposition. Thirdly, we give explicit $A_{\infty}$-multiplication formulas for both the Hochschild cochain complex and the Hochschild chain complex under additive decompositions. Finally, we give $A_{\infty}$-multiplication formulas in the context of abelian groups. |
| title | $A_{\infty}$-structures on the additive decomposition of the Tate-Hochschild cohomology of a finite group algebra |
| topic | K-Theory and Homology Rings and Algebras 16E40, 20J06, 18G70, |
| url | https://arxiv.org/abs/2601.00351 |