Automorphism groups of Weyl algebras

TL;DR

This paper proves a conjecture that the automorphism group of the Weyl algebra is isomorphic to the Poisson automorphism group of the Poisson Weyl algebra, establishing a deep connection between these algebraic structures.

Contribution

It confirms Kanel-Belov and Kontsevich's conjecture, demonstrating an isomorphism between automorphism groups of Weyl and Poisson Weyl algebras.

Findings

Automorphism group of Weyl algebra is isomorphic to Poisson automorphism group of Poisson Weyl algebra

Proof of Kanel-Belov and Kontsevich's conjecture

Establishes a fundamental link between Weyl and Poisson algebra structures

Abstract

Kanel-Belov and Kontsevich's conjecture in \cite[Conjecture 1]{BeKo} is proved: The automorphism group of the $n$-th Weyl algebra is isomorphic to the Poisson automorphism group of the $n$-th Poisson Weyl algebra.