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Permanent link (DOI): https://doi.org/10.7939/R3XG9FK5W

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Diagonalizable subalgebras of the first Weyl algebra Open Access

Descriptions

Other title
Subject/Keyword
Weyl algebra
Type of item
Thesis
Degree grantor
University of Alberta
Author or creator
Tan, Xiaobai
Supervisor and department
Kuttler, Jochen (Mathematical Science) Pianzola, Arturo (Mathematical Science)
Examining committee member and department
Nascimento, Mario (Computing Science)
Department
Department of Mathematical and Statistical Sciences
Specialization

Date accepted
2009-10-02T15:34:26Z
Graduation date
2009-11
Degree
Master of Science
Degree level
Master's
Abstract
Let $A_1$ denote the first Weyl algebra over a field $K$ of characteristic 0; that is, $A_1$ is generated over $K$ by elements $p$, $q$ that satisfy the relation $pq-qp=1$. One can view $A_1$ as an algebra of differential operators by setting $q=X$, $p=d/dX$. The basic questions which are addressed in this paper is what are all the maximal diagonalizable subalgebras of $A_1$ and if $K$ is not algebraically closed, what conditions should be placed on the element $x\in A_1$ so that $x$ is diagonalizable on $A_1$. Thus, we use these diagonalizable elements to verify the Jacobian conjecture for $n=1$.
Language
English
DOI
doi:10.7939/R3XG9FK5W
Rights
This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for the purpose of private, scholarly or scientific research. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.
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