Short Star-Products for Filtered Quantizations, I
We develop a theory of short star-products for filtered quantizations of graded Poisson algebras, introduced in 2016 by Beem, Peelaers, and Rastelli for algebras of regular functions on hyperKähler cones in the context of 3-dimensional N = 4 superconformal field theories [Beem C., Peelaers W., Raste...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2020 |
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| Format: | Artikel |
| Sprache: | English |
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Інститут математики НАН України
2020
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/210596 |
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| Zitieren: | Short Star-Products for Filtered Quantizations, I. Pavel Etingof and Douglas Stryker. SIGMA 16 (2020), 014, 28 pages |
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Etingof, Pavel Stryker, Douglas 2025-12-12T10:35:54Z 2020 Short Star-Products for Filtered Quantizations, I. Pavel Etingof and Douglas Stryker. SIGMA 16 (2020), 014, 28 pages 1815-0659 2020 Mathematics Subject Classification: 06B15; 53D55 arXiv:1909.13588 https://nasplib.isofts.kiev.ua/handle/123456789/210596 https://doi.org/10.3842/SIGMA.2020.014 We develop a theory of short star-products for filtered quantizations of graded Poisson algebras, introduced in 2016 by Beem, Peelaers, and Rastelli for algebras of regular functions on hyperKähler cones in the context of 3-dimensional N = 4 superconformal field theories [Beem C., Peelaers W., Rastelli L., Comm. Math. Phys. 354 (2017), 345-392]. This appears to be a new structure in representation theory, which is an algebraic incarnation of the non-holomorphic SU(2)-symmetry of such cones. Using the technique of twisted traces on quantizations (an idea due to Kontsevich), we prove the conjecture by Beem, Peelaers, and Rastelli that short star-products depend on finitely many parameters (under a natural nondegeneracy condition), and also construct these star products in a number of examples, confirming another conjecture by Beem, Peelaers, and Rastelli. The first author is grateful to C. Beem and A. Kapustin for introducing him to the problem, M.Kontsevich for contributing a key idea, and C. Beem, M. Dedushenko, D. Gaiotto, D. Kaledin, D. Kazhdan, I. Losev, G. Lusztig, H. Nakajima, E. Rains, L. Rastelli, and T. Schedler for useful discussions. The work of the first author was partially supported by the NSF grant DMS1502244. The work of the second author was supported by the MIT UROP (Undergraduate Research Opportunities Program). en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Short Star-Products for Filtered Quantizations, I Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Short Star-Products for Filtered Quantizations, I |
| spellingShingle |
Short Star-Products for Filtered Quantizations, I Etingof, Pavel Stryker, Douglas |
| title_short |
Short Star-Products for Filtered Quantizations, I |
| title_full |
Short Star-Products for Filtered Quantizations, I |
| title_fullStr |
Short Star-Products for Filtered Quantizations, I |
| title_full_unstemmed |
Short Star-Products for Filtered Quantizations, I |
| title_sort |
short star-products for filtered quantizations, i |
| author |
Etingof, Pavel Stryker, Douglas |
| author_facet |
Etingof, Pavel Stryker, Douglas |
| publishDate |
2020 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
We develop a theory of short star-products for filtered quantizations of graded Poisson algebras, introduced in 2016 by Beem, Peelaers, and Rastelli for algebras of regular functions on hyperKähler cones in the context of 3-dimensional N = 4 superconformal field theories [Beem C., Peelaers W., Rastelli L., Comm. Math. Phys. 354 (2017), 345-392]. This appears to be a new structure in representation theory, which is an algebraic incarnation of the non-holomorphic SU(2)-symmetry of such cones. Using the technique of twisted traces on quantizations (an idea due to Kontsevich), we prove the conjecture by Beem, Peelaers, and Rastelli that short star-products depend on finitely many parameters (under a natural nondegeneracy condition), and also construct these star products in a number of examples, confirming another conjecture by Beem, Peelaers, and Rastelli.
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| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/210596 |
| citation_txt |
Short Star-Products for Filtered Quantizations, I. Pavel Etingof and Douglas Stryker. SIGMA 16 (2020), 014, 28 pages |
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AT etingofpavel shortstarproductsforfilteredquantizationsi AT strykerdouglas shortstarproductsforfilteredquantizationsi |
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2025-12-17T12:03:35Z |
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2025-12-17T12:03:35Z |
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