Usage
  • 18 views
  • 2 downloads

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 $pq-qp=1$. 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 $n=1$.

  • Subjects / Keywords
  • Graduation date
    2009-11
  • 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.
  • Language
    English
  • Institution
    University of Alberta
  • Degree level
    Master's
  • Department
    • Department of Mathematical and Statistical Sciences
  • Supervisor / co-supervisor and their department(s)
    • Kuttler, Jochen (Mathematical Science) Pianzola, Arturo (Mathematical Science)
  • Examining committee members and their departments
    • Nascimento, Mario (Computing Science)