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Diagonalizable subalgebras of the first Weyl algebra

 Author / Creator
 Tan, Xiaobai

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 $pqqp=1$. 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 $n=1$.

 Subjects / Keywords

 Graduation date
 200911

 Type of Item
 Thesis

 Degree
 Master of Science

 License
 This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for noncommercial purposes. 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.