Replacing bar-like resolutions in a simplicial setting
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866916198521765888 |
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| author | Carolus, Samuel Laubacher, Jacob Vitalbo, Sydney D. Widlarz, Leah K. |
| author_facet | Carolus, Samuel Laubacher, Jacob Vitalbo, Sydney D. Widlarz, Leah K. |
| contents | It is well known that the bar resolution can be replaced with any projective resolution of the corresponding algebra when computing the Hochschild (co)homology of that algebra. This is, in fact, a feature of its construction via derived functors. For generalizations and extensions of the Hochschild (co)homology, one uses a bar-like resolution in a simplicial setting in order to accommodate the changing module structures in every dimension. In this note, we present a method in order to replace these bar-like resolutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_06368 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Replacing bar-like resolutions in a simplicial setting Carolus, Samuel Laubacher, Jacob Vitalbo, Sydney D. Widlarz, Leah K. Rings and Algebras Primary 18G31, Secondary 16E40, 16E05, 18G10 It is well known that the bar resolution can be replaced with any projective resolution of the corresponding algebra when computing the Hochschild (co)homology of that algebra. This is, in fact, a feature of its construction via derived functors. For generalizations and extensions of the Hochschild (co)homology, one uses a bar-like resolution in a simplicial setting in order to accommodate the changing module structures in every dimension. In this note, we present a method in order to replace these bar-like resolutions. |
| title | Replacing bar-like resolutions in a simplicial setting |
| topic | Rings and Algebras Primary 18G31, Secondary 16E40, 16E05, 18G10 |
| url | https://arxiv.org/abs/2404.06368 |