Quantisation of derived Poisson structures
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2017
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| _version_ | 1866909844951269376 |
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| author | Pridham, J. P. |
| author_facet | Pridham, J. P. |
| contents | We prove that every $0$-shifted Poisson structure on a derived Artin $n$-stack admits a curved $A_{\infty}$ deformation quantisation whenever the stack has perfect cotangent complex; in particular, this applies to LCI schemes, where it gives a DQ algebroid quantisation. Whereas the Kontsevich--Tamarkin approach to quantisation for smooth varieties hinges on invariance of the Hochschild complex under affine transformations, we instead exploit the observation that the Hochschild complex carries an anti-involution, and that such anti-involutive deformations of the complex of polyvectors are essentially unique. We also establish analogous statements for deformation quantisations in $\mathcal{C}^{\infty}$ and analytic settings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1708_00496 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Quantisation of derived Poisson structures Pridham, J. P. Algebraic Geometry Quantum Algebra We prove that every $0$-shifted Poisson structure on a derived Artin $n$-stack admits a curved $A_{\infty}$ deformation quantisation whenever the stack has perfect cotangent complex; in particular, this applies to LCI schemes, where it gives a DQ algebroid quantisation. Whereas the Kontsevich--Tamarkin approach to quantisation for smooth varieties hinges on invariance of the Hochschild complex under affine transformations, we instead exploit the observation that the Hochschild complex carries an anti-involution, and that such anti-involutive deformations of the complex of polyvectors are essentially unique. We also establish analogous statements for deformation quantisations in $\mathcal{C}^{\infty}$ and analytic settings. |
| title | Quantisation of derived Poisson structures |
| topic | Algebraic Geometry Quantum Algebra |
| url | https://arxiv.org/abs/1708.00496 |