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Mathematics > Algebraic Geometry

arXiv:1812.02859 (math)
[Submitted on 7 Dec 2018 (v1), last revised 2 Dec 2020 (this version, v7)]

Title:Augmented Polynomial Symplectomorphisms and Quantization

Authors:Alexei Kanel-Belov, Andrey Elishev, Jie-Tai Yu
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Abstract:The objective of this paper is the proof of a conjecture of Kontsevich on the isomorphism between groups of polynomial symplectomorphisms and automorphisms of the corresponding Weyl algebra in characteristic zero. The proof is based on the study of topological properties of automorphism $\Ind$-varieties of the so-called augmented and skew augmented versions of Poisson and Weyl algebras. Approximation by tame automorphisms as well as a certain singularity analysis procedure is utilized in the construction of the lifting of augmented polynomial symplectomorphisms, after which specialization of the augmentation parameter is performed in order to obtain the main result.
Comments: 34 pages; essential revisions. arXiv admin note: substantial text overlap with arXiv:1512.06533
Subjects: Algebraic Geometry (math.AG)
MSC classes: 14R10
Cite as: arXiv:1812.02859 [math.AG]
  (or arXiv:1812.02859v7 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.1812.02859

Submission history

From: Alexei Kanel-Belov Prof. [view email]
[v1] Fri, 7 Dec 2018 00:19:46 UTC (20 KB)
[v2] Thu, 13 Dec 2018 01:09:51 UTC (22 KB)
[v3] Sat, 22 Dec 2018 22:11:46 UTC (22 KB)
[v4] Wed, 27 Feb 2019 19:46:05 UTC (23 KB)
[v5] Mon, 9 Sep 2019 19:15:53 UTC (31 KB)
[v6] Tue, 11 Feb 2020 14:49:34 UTC (31 KB)
[v7] Wed, 2 Dec 2020 06:51:56 UTC (31 KB)
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