Corings, their dual rings and relative (co)Hochschild cohomology
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915446730522624 |
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| author | Lindell, Jonathan |
| author_facet | Lindell, Jonathan |
| contents | We show for a coring which is finitely generated projective as a left module that the Cartier cohomology is isomorphic to the relative Hochschild cohomology of the right algebra. Furthermore, we show that this isomorphism lifts to the level of $B_{\infty}$-algebras of the chain complexes, by showing that the opposite $B_{\infty}$-algebra of the relative Hochschild cochains of the right algebra is isomorphic to the $B_{\infty}$-algebra of Cartier cochains. Lastly, we apply this to entwining structures where the coalgebra is finite-dimensional, to get a description of the equivariant cohomology of the entwining structure as the relative Hochschild cohomology of the twisted convolution algebra. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_10668 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Corings, their dual rings and relative (co)Hochschild cohomology Lindell, Jonathan K-Theory and Homology Rings and Algebras 16E40 (Primary) 16T15 We show for a coring which is finitely generated projective as a left module that the Cartier cohomology is isomorphic to the relative Hochschild cohomology of the right algebra. Furthermore, we show that this isomorphism lifts to the level of $B_{\infty}$-algebras of the chain complexes, by showing that the opposite $B_{\infty}$-algebra of the relative Hochschild cochains of the right algebra is isomorphic to the $B_{\infty}$-algebra of Cartier cochains. Lastly, we apply this to entwining structures where the coalgebra is finite-dimensional, to get a description of the equivariant cohomology of the entwining structure as the relative Hochschild cohomology of the twisted convolution algebra. |
| title | Corings, their dual rings and relative (co)Hochschild cohomology |
| topic | K-Theory and Homology Rings and Algebras 16E40 (Primary) 16T15 |
| url | https://arxiv.org/abs/2508.10668 |