Are there unique factorizations for weyl algebras?











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I just read about Weyl algebras, and they sound like neat little toys that are similar in a number of ways to polynomials. However, it's curious to me that they are non-commutative, and I was wondering if there are unique factorizations for Weyl algebras the way there are for Hurwitz quaternions.



Further, there's a polynomial time factorization algorithm for polynomials, and at first glance Weyl algebras are extensions of polynomials. Do they have polynomial time factorization algorithms?










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    up vote
    4
    down vote

    favorite
    1












    I just read about Weyl algebras, and they sound like neat little toys that are similar in a number of ways to polynomials. However, it's curious to me that they are non-commutative, and I was wondering if there are unique factorizations for Weyl algebras the way there are for Hurwitz quaternions.



    Further, there's a polynomial time factorization algorithm for polynomials, and at first glance Weyl algebras are extensions of polynomials. Do they have polynomial time factorization algorithms?










    share|cite|improve this question


























      up vote
      4
      down vote

      favorite
      1









      up vote
      4
      down vote

      favorite
      1






      1





      I just read about Weyl algebras, and they sound like neat little toys that are similar in a number of ways to polynomials. However, it's curious to me that they are non-commutative, and I was wondering if there are unique factorizations for Weyl algebras the way there are for Hurwitz quaternions.



      Further, there's a polynomial time factorization algorithm for polynomials, and at first glance Weyl algebras are extensions of polynomials. Do they have polynomial time factorization algorithms?










      share|cite|improve this question















      I just read about Weyl algebras, and they sound like neat little toys that are similar in a number of ways to polynomials. However, it's curious to me that they are non-commutative, and I was wondering if there are unique factorizations for Weyl algebras the way there are for Hurwitz quaternions.



      Further, there's a polynomial time factorization algorithm for polynomials, and at first glance Weyl algebras are extensions of polynomials. Do they have polynomial time factorization algorithms?







      algebraic-number-theory prime-factorization






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      share|cite|improve this question













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      share|cite|improve this question








      edited Nov 22 at 12:34









      amWhy

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      191k28224439










      asked Apr 24 '14 at 19:32









      dezakin

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      1,148922



























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