Cyclic duality between BV algebras and BV modules
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arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866929479955251200 |
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| author | Kowalzig, Niels |
| author_facet | Kowalzig, Niels |
| contents | We show that if an operad is at the same time a cosimplicial object such that the respective structure maps are compatible with the operadic composition in a natural way, then one obtains a Gerstenhaber algebra structure on cohomology, and if the operad is cyclic, even that of a BV algebra. In particular, if a cyclic opposite module over an operad with multiplication is itself a cyclic operad that meets the cosimplicial compatibility conditions, the cohomology of its cyclic dual turns into a BV algebra. This amounts to conditions for when the cyclic dual of a BV module is endowed with a BV algebra structure, a result we exemplify by looking at classical and less classical (co)homology groups in Hopf algebra theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_15278 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Cyclic duality between BV algebras and BV modules Kowalzig, Niels Algebraic Topology K-Theory and Homology Quantum Algebra Rings and Algebras We show that if an operad is at the same time a cosimplicial object such that the respective structure maps are compatible with the operadic composition in a natural way, then one obtains a Gerstenhaber algebra structure on cohomology, and if the operad is cyclic, even that of a BV algebra. In particular, if a cyclic opposite module over an operad with multiplication is itself a cyclic operad that meets the cosimplicial compatibility conditions, the cohomology of its cyclic dual turns into a BV algebra. This amounts to conditions for when the cyclic dual of a BV module is endowed with a BV algebra structure, a result we exemplify by looking at classical and less classical (co)homology groups in Hopf algebra theory. |
| title | Cyclic duality between BV algebras and BV modules |
| topic | Algebraic Topology K-Theory and Homology Quantum Algebra Rings and Algebras |
| url | https://arxiv.org/abs/2312.15278 |