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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 $pq-qp=1$. 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
2009-11
• Type of Item
Thesis
• Degree
Master of Science
• DOI
https://doi.org/10.7939/R3XG9FK5W