Finitely generated bimodules over Weyl algebras

Niels Lauritzen, Jesper Funch Thomsen

Published 2023-08-18Version 1

Affine space over the complex numbers is simply connected in the sense that it does not afford any non-trivial \'etale finite covers. In this paper we prove the non-commutative analogue of this statement: an endomorphism of a Weyl algebra provides a natural holonomic bimodule structure on the Weyl algebra. If this bimodule is finitely generated from the left or right, then the endomorphism is an automorphism. Finite generation of this bimodule in large positive characteristics is equivalent to the Dixmier conjecture.