Pre-Calabi-Yau algebras and oriented gravity properad
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915145269116928 |
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| author | Merkulov, Sergei |
| author_facet | Merkulov, Sergei |
| contents | We study the dual cyclic Hochschild complex $Cyc^\bullet(A,\mathbb{K})$ of a (possibly, infinite-dimensional) $A_\infty$-algebra $(A,μ)$ and prove that any pre-Calabi-Yau extension $π$ of the given $A_\infty$ structure $μ$ in $A$ induces on the cyclic cohomology of $(A,μ)$ a representation of a new dg properad of oriented ribbon graphs. We compute the cohomology of that properad in terms of the compactly supported cohomology groups of moduli spaces $\mathcal{M}_{g,m+n}$ of algebraic curves of genus $g$ with $m+n$ marked points.
We also show that the gravity operad acts naturally on the higher Hochschild cohomology of any pre-CY algebra $(A, π)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_11158 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Pre-Calabi-Yau algebras and oriented gravity properad Merkulov, Sergei Quantum Algebra We study the dual cyclic Hochschild complex $Cyc^\bullet(A,\mathbb{K})$ of a (possibly, infinite-dimensional) $A_\infty$-algebra $(A,μ)$ and prove that any pre-Calabi-Yau extension $π$ of the given $A_\infty$ structure $μ$ in $A$ induces on the cyclic cohomology of $(A,μ)$ a representation of a new dg properad of oriented ribbon graphs. We compute the cohomology of that properad in terms of the compactly supported cohomology groups of moduli spaces $\mathcal{M}_{g,m+n}$ of algebraic curves of genus $g$ with $m+n$ marked points. We also show that the gravity operad acts naturally on the higher Hochschild cohomology of any pre-CY algebra $(A, π)$. |
| title | Pre-Calabi-Yau algebras and oriented gravity properad |
| topic | Quantum Algebra |
| url | https://arxiv.org/abs/2501.11158 |