2018/02/05 by Alexei Kanel-Belov, Kanel-Belov, Alexei, Andrey Elishev +3
Mathematics · #Advanced Algebra and Geometry #Advanced Differential Equations and Dynamical Systems #Advanced Topics in Algebra #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA
paper · pdf · doi:10.48550/arxiv.1802.01225
11 pages, preliminary version
arxiv created 2018/02/05 · openalex publication_date 2018/02/05 · arxiv updated 2018/02/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We outline the proof of a conjecture of Kontsevich on the isomorphism between the group of polynomial symplectomorphisms in 2n variables and the group of automorphisms of the n-th Weyl algebra over complex numbers. Our proof uses lifting of polynomial symplectomorphisms to Weyl algebra automorphisms by means of approximation by tame symplectomorphisms and gauging of the lifted morphism. Approximation by tame symplectomorphisms is the symplectic version of the well-known theorem of D. Anick and is a result of our prior work.