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ЖУРНАЛЫ // Symmetry, Integrability and Geometry: Methods and Applications // Архив

SIGMA, 2020, том 16, 014, 28 стр. (Mi sigma1551)

Эта публикация цитируется в 8 статьях

Short Star-Products for Filtered Quantizations, I

Pavel Etingof, Douglas Stryker

Department of Mathematics, MIT, Cambridge, MA 02139, USA

Аннотация: 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.

Ключевые слова: star-product, quantization, hyperKähler cone, symplectic singularity.

MSC: 06B15; 53D55

Поступила: 1 октября 2019 г.; в окончательном варианте 1 марта 2020 г.; опубликована 11 марта 2020 г.

Язык публикации: английский

DOI: 10.3842/SIGMA.2020.014



Реферативные базы данных:
ArXiv: 1909.13588


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