Symmetry, Integrability and Geometry: Methods and Applications
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



SIGMA:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


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
\Bibitem{EtiStr20}
\by Pavel~Etingof, Douglas~Stryker
\paper Short Star-Products for Filtered Quantizations,~I
\jour SIGMA
\yr 2020
\vol 16
\papernumber 014
\totalpages 28
\mathnet{http://mi.mathnet.ru/sigma1551}
\crossref{https://doi.org/10.3842/SIGMA.2020.014}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000519575700001}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85082424979}
Linking options:
  • https://www.mathnet.ru/eng/sigma1551
  • https://www.mathnet.ru/eng/sigma/v16/p14
  • 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
    Statistics & downloads:
    Abstract page:115
    Full-text PDF :28
    References:22
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024