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
Datum:2020
Hauptverfasser: Etingof, Pavel, Stryker, Douglas
Format: Artikel
Sprache:English
Veröffentlicht: Інститут математики НАН України 2020
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

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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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.
ISSN:1815-0659