Diagonalizable subalgebras of the first Weyl algebra

• Author / Creator

  Tan, Xiaobai

• Let $A1$ denote the first Weyl algebra over a field $K$ of characteristic 0; that is, $A1$ is generated over $K$ by elements $p$, $q$ that satisfy the relation $pq-qp=1$. One can view $A1$ 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 $A1$ and if $K$ is not algebraically closed, what conditions should be placed on the element $x\in A1$ so that $x$ is diagonalizable on $A1$. Thus, we use these diagonalizable elements to verify the Jacobian conjecture for $n=1$.

• Subjects / Keywords

  • Weyl algebra

• Graduation date

  Fall 2009

• Type of Item

  Thesis

• Degree

  Master of Science

• DOI

  https://doi.org/10.7939/R3XG9FK5W

• License

  This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial 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.