Présentation jordanienne de l'algèbre de Weyl $A_2$
Volume 76 / 2001
Annales Polonici Mathematici 76 (2001), 1-9
MSC: 16S32, 16W35, 16S36.
DOI: 10.4064/ap76-1-1
Abstract
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 $a=b$.
