Homology of Epsilon-Strongly Graded Algebras
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909700054843392 |
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| author | Jerez, Emmanuel |
| author_facet | Jerez, Emmanuel |
| contents | Let $G$ be a group and $S$ a unital epsilon-strongly $G$-graded algebra. We construct spectral sequences converging to the Hochschild (co)homology of $S$. Each spectral sequence is expressed in terms of the partial group (co)homology of $G$ with coefficients in the Hochschild (co)homology of the degree-one component of $S$. Moreover, we show that the homology spectral sequence decomposes according to the conjugacy classes of $G$, and, by means of the globalization functor, its $E^2$-page can be identified with the ordinary group homology of suitable centralizers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_16778 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Homology of Epsilon-Strongly Graded Algebras Jerez, Emmanuel K-Theory and Homology Rings and Algebras Primary 16E40, 16W50, Secondary 16W22, 18G40, 18G60 Let $G$ be a group and $S$ a unital epsilon-strongly $G$-graded algebra. We construct spectral sequences converging to the Hochschild (co)homology of $S$. Each spectral sequence is expressed in terms of the partial group (co)homology of $G$ with coefficients in the Hochschild (co)homology of the degree-one component of $S$. Moreover, we show that the homology spectral sequence decomposes according to the conjugacy classes of $G$, and, by means of the globalization functor, its $E^2$-page can be identified with the ordinary group homology of suitable centralizers. |
| title | Homology of Epsilon-Strongly Graded Algebras |
| topic | K-Theory and Homology Rings and Algebras Primary 16E40, 16W50, Secondary 16W22, 18G40, 18G60 |
| url | https://arxiv.org/abs/2507.16778 |