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The graph of a Weyl algebra endomorphism

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The graph of a Weyl algebra endomorphism. / Lauritzen, Niels; Thomsen, Jesper Funch.

I: Bulletin of the London Mathematical Society, Bind 53, Nr. 1, 02.2021, s. 161-176.

Publikation: Bidrag til tidsskrift/Konferencebidrag i tidsskrift /Bidrag til avisTidsskriftartikelForskningpeer review

Harvard

Lauritzen, N & Thomsen, JF 2021, 'The graph of a Weyl algebra endomorphism', Bulletin of the London Mathematical Society, bind 53, nr. 1, s. 161-176. https://doi.org/10.1112/blms.12408

APA

Lauritzen, N., & Thomsen, J. F. (2021). The graph of a Weyl algebra endomorphism. Bulletin of the London Mathematical Society, 53(1), 161-176. https://doi.org/10.1112/blms.12408

CBE

Lauritzen N, Thomsen JF. 2021. The graph of a Weyl algebra endomorphism. Bulletin of the London Mathematical Society. 53(1):161-176. https://doi.org/10.1112/blms.12408

MLA

Vancouver

Lauritzen N, Thomsen JF. The graph of a Weyl algebra endomorphism. Bulletin of the London Mathematical Society. 2021 feb.;53(1):161-176. https://doi.org/10.1112/blms.12408

Author

Lauritzen, Niels ; Thomsen, Jesper Funch. / The graph of a Weyl algebra endomorphism. I: Bulletin of the London Mathematical Society. 2021 ; Bind 53, Nr. 1. s. 161-176.

Bibtex

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title = "The graph of a Weyl algebra endomorphism",
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 Gr{\"o}bner basis algorithm for detecting invertibility of an endomorphism for Weyl algebras and computing the inverse over arbitrary fields.",
keywords = "16D20, 16S32 (primary), 16W20 (secondary)",
author = "Niels Lauritzen and Thomsen, {Jesper Funch}",
year = "2021",
month = feb,
doi = "10.1112/blms.12408",
language = "English",
volume = "53",
pages = "161--176",
journal = "Bulletin of the London Mathematical Society",
issn = "0024-6093",
publisher = "Oxford University Press",
number = "1",

}

RIS

TY - JOUR

T1 - The graph of a Weyl algebra endomorphism

AU - Lauritzen, Niels

AU - Thomsen, Jesper Funch

PY - 2021/2

Y1 - 2021/2

N2 - 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.

AB - 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.

KW - 16D20

KW - 16S32 (primary)

KW - 16W20 (secondary)

UR - http://www.scopus.com/inward/record.url?scp=85090302635&partnerID=8YFLogxK

U2 - 10.1112/blms.12408

DO - 10.1112/blms.12408

M3 - Journal article

VL - 53

SP - 161

EP - 176

JO - Bulletin of the London Mathematical Society

JF - Bulletin of the London Mathematical Society

SN - 0024-6093

IS - 1

ER -