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 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Інститут математики НАН України
2020
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/210596 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Short Star-Products for Filtered Quantizations, I. Pavel Etingof and Douglas Stryker. SIGMA 16 (2020), 014, 28 pages |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | 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 |