The graph of a Weyl algebra endomorphism

Niels Lauritzen; Jesper Funch Thomsen

doi:10.1112/blms.12408

The graph of a Weyl algebra endomorphism

Niels Lauritzen^*, Jesper Funch Thomsen^*

^*Corresponding author af dette arbejde

Institut for Matematik

Publikation: Bidrag til tidsskrift/Konferencebidrag i tidsskrift /Bidrag til avis › Tidsskriftartikel › Forskning › peer review

Abstract

Endomorphisms of Weyl algebras are studied using bimodules. Initially, for a Weyl algebra over a field of characteristic zero, Bernstein's inequality implies that holonomic bimodules finitely generated from the right (respectively, left) form a monoidal category. The most important bimodule in this paper is the graph of an endomorphism. We prove that the graph of an endomorphism of a Weyl algebra over a field of characteristic zero is a simple bimodule. The simplicity of the tensor product of the dual graph and the graph is equivalent to the Dixmier conjecture. It is also shown how the graph construction leads to a non-commutative Gröbner basis algorithm for detecting invertibility of an endomorphism for Weyl algebras and computing the inverse over arbitrary fields.

Originalsprog	Engelsk
Tidsskrift	Bulletin of the London Mathematical Society
Vol/bind	53
Nummer	1
Sider (fra-til)	161-176
Antal sider	16
ISSN	0024-6093
DOI	https://doi.org/10.1112/blms.12408
Status	Udgivet - feb. 2021

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10.1112/blms.12408

https://arxiv.org/pdf/1904.03128.pdf

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The graph of a Weyl algebra endomorphism

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