Batalin-Vilkovisky structure on Hochschild cohomology with coefficients in the dual algebra
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2018
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| _version_ | 1866915189920628736 |
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| author | Armenta, Marco Leblanc, Samuel |
| author_facet | Armenta, Marco Leblanc, Samuel |
| contents | We prove that Hochschild cohomology with coefficients in $A^*=\Hom_k(A,k)$ under conditions on the algebra structure of $A^*$ is a Batalin-Vilkovisky algebra. We also show that for symmetric and Frobenius algebras, this recovers the known BV-structures in Hochschild cohomology with coefficients in $A$ but admits an easy-to-describe BV-operator. Finally, we show that for monomial algebras $A = kQ/\langle T \rangle$, the Hochschild cohomology with coefficients in $A^*$ is always a Batalin-Vilkovisky algebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1810_13023 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Batalin-Vilkovisky structure on Hochschild cohomology with coefficients in the dual algebra Armenta, Marco Leblanc, Samuel K-Theory and Homology 16E40 (primary) 16G20 (secondary) We prove that Hochschild cohomology with coefficients in $A^*=\Hom_k(A,k)$ under conditions on the algebra structure of $A^*$ is a Batalin-Vilkovisky algebra. We also show that for symmetric and Frobenius algebras, this recovers the known BV-structures in Hochschild cohomology with coefficients in $A$ but admits an easy-to-describe BV-operator. Finally, we show that for monomial algebras $A = kQ/\langle T \rangle$, the Hochschild cohomology with coefficients in $A^*$ is always a Batalin-Vilkovisky algebra. |
| title | Batalin-Vilkovisky structure on Hochschild cohomology with coefficients in the dual algebra |
| topic | K-Theory and Homology 16E40 (primary) 16G20 (secondary) |
| url | https://arxiv.org/abs/1810.13023 |