Automorphism groups of Weyl algebras
No-Ho Myung, Sei-Qwon Oh

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 -th Weyl algebra is isomorphic to the Poisson automorphism group of the -th Poisson Weyl algebra.
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Taxonomy
Topicsadvanced mathematical theories
