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Automorphisms of the Weyl algebra. (English) Zbl 1081.16031

Summary: 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.

MSC:

16S36 Ordinary and skew polynomial rings and semigroup rings
16W20 Automorphisms and endomorphisms
16S32 Rings of differential operators (associative algebraic aspects)
17B63 Poisson algebras
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References:

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