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
  • Graduation date
    Fall 2009
  • Type of Item
  • Degree
    Master of Science
  • DOI
  • License
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