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Symmetry, Integrability and Geometry: Methods and Applications, 2020, Volume 16, 014, 28 pp.
DOI: https://doi.org/10.3842/SIGMA.2020.014
(Mi sigma1551)
 

This article is cited in 8 scientific papers (total in 8 papers)

Short Star-Products for Filtered Quantizations, I

Pavel Etingof, Douglas Stryker

Department of Mathematics, MIT, Cambridge, MA 02139, USA
Full-text PDF (541 kB) Citations (8)
References:
Abstract: 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 ${\rm SU}(2)$-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.
Keywords: star-product, quantization, hyperKähler cone, symplectic singularity.
Funding agency Grant number
National Science Foundation DMS-1502244
The work of the first author was partially supported by the NSF grant DMS-1502244. The work of the second author was supported by the MIT UROP (Undergraduate Research Opportunities Program).
Received: October 1, 2019; in final form March 1, 2020; Published online March 11, 2020
Bibliographic databases:
Document Type: Article
MSC: 06B15; 53D55
Language: English
Citation: Pavel Etingof, Douglas Stryker, “Short Star-Products for Filtered Quantizations, I”, SIGMA, 16 (2020), 014, 28 pp.
Citation in format AMSBIB
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\by Pavel~Etingof, Douglas~Stryker
\paper Short Star-Products for Filtered Quantizations,~I
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\vol 16
\papernumber 014
\totalpages 28
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  • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Symmetry, Integrability and Geometry: Methods and Applications
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    Abstract page:116
    Full-text PDF :28
    References:22
     
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