Présentation jordanienne de l'algèbre de Weyl $A_2$

Volume 76 / 2001

J. Alev, F. Dumas Annales Polonici Mathematici 76 (2001), 1-9 MSC: 16S32, 16W35, 16S36. DOI: 10.4064/ap76-1-1


Let $k$ be a commutative field. For any $a,b\in k$, we denote by $J_{a,b}(k)$ the deformation of the 2-dimensional Weyl algebra over $k$ associated with the Jordanian Hecke symmetry with parameters $a$ and $b$. We prove that: (i) any $J_{a,b}(k)$ can be embedded in the usual Weyl algebra $A_2(k)$, and (ii) $J_{a,b}(k)$ is isomorphic to $A_2(k)$ if and only if $a=b$.


  • J. AlevUniversité de Reims
    Mathématiques, U.M.R. 6056
    B.P. 1039
    51687 Reims Cedex, France
  • F. DumasUniversité Blaise Pascal (Clermont-Ferrand 2)
    Laboratoire de Mathématiques Pures
    63177 Aubière Cedex, France

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