Automorphisms of the Weyl Algebra

By A. Belov-Kanel, M. Kontsevich. 2005

125 citations recorded by the source corpus.

We discuss a conjecture which says that the automorphism group of the Weyl algebra in characteristic zero is canonically isomorphic to the automorphism group of the corresponding Poisson algebra of classical polynomial symbols. Several arguments in favor of this conjecture are presented, all based on the consideration of the reduction of the Weyl algebra to positive characteristic

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/d30e9f38314e1165aad2bd778fd7da603380f5bd

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In Discrete Mathematics and Combinatorics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Holonomic -modules and positive characteristic (2009, unknown): “A corollary of conjecture 5 is one of conjectures discussed in [3], which says that for any polynomial symplectomorphism φ of A2n k there exists a canonically associated to it a bimodule Mφ over the Weyl algebra An,k giving Morita selfequivalence of the category of An,k-modules.”
Universal enveloping algebras and universal derivations of Poisson algebras (2011, background): “he Poisson symplectic algebra Pn and the Weyl algebra An are isomorphic. It is not diﬃcult to show that this result is true also for ﬁelds of positive characteristic. A. Belov-Kanel and M. Kontsevich [4] formulated the next problem. Problem 1. The automorphism group of the Weyl algebra of index nis ”
Branes and Quantization (2008, background): “holomorphic functions, not just a formal deformation (see [ 23 ] for a detailed discussion of”