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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
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.
Received: October 1, 2019; in final form March 1, 2020; Published online March 11, 2020
Citation:
Pavel Etingof, Douglas Stryker, “Short Star-Products for Filtered Quantizations, I”, SIGMA, 16 (2020), 014, 28 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1551 https://www.mathnet.ru/eng/sigma/v16/p14
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Abstract page: | 116 | Full-text PDF : | 28 | References: | 22 |
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