Bavula, V.V. (2011) On the eigenvector algebra of the product of elements with commutator one in the first Weyl algebra. Mathematical Proceedings of the Cambridge Philosophical Society, 151 (2). pp. 245-262. ISSN 0305-0041
Abstract
Let A1 = K〈X, Y|[Y, X]=1〉 be the (first) Weyl algebra over a field K of characteristic zero. It is known that the set of eigenvalues of the inner derivation ad(YX) of A1 is ℤ. Let A1 → A1, X ↦ x, Y ↦ y, be a K-algebra homomorphism, i.e. [y, x] = 1. It is proved that the set of eigenvalues of the inner derivation ad(yx) of the Weyl algebra A1 is ℤ and the eigenvector algebra of ad(yx) is K〈x, y〉 (this would be an easy corollary of the Problem/Conjecture of Dixmier of 1968 [still open]: is an algebra endomorphism of A1 an automorphism?).
Metadata
Item Type: | Article |
---|---|
Authors/Creators: |
|
Copyright, Publisher and Additional Information: | © Cambridge Philosophical Society 2011. This is an author produced version of a paper subsequently published in Mathematical Proceedings of the Cambridge Philosophical Society. Uploaded in accordance with the publisher's self-archiving policy. |
Dates: |
|
Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 16 Feb 2018 12:09 |
Last Modified: | 14 Mar 2023 15:16 |
Published Version: | https://doi.org/10.1017/S0305004111000491 |
Status: | Published |
Publisher: | Cambridge University Press |
Refereed: | Yes |
Identification Number: | 10.1017/S0305004111000491 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:127442 |