Finite-dimensional Lie subalgebras of the Weyl algebra
de Traubenberg, M. Rausch ; Slupinski, M. J. ; Tanasa, A.
arXiv, 0504224 / Harvested from arXiv
Text on arXiv
We classify up to isomorphism all finite-dimensional Lie algebras that can be realised as Lie subalgebras of the complex Weyl algebra $A_1$. The list we obtain turns out to be discrete and for example, the only non-solvable Lie algebras with this property are: $sl(2)$, $sl(2)\times\mathbb C$ and $sl(2)\ltimes{\cal H}_3$. We then give several different characterisations, normal forms and isotropy groups for the action of $Aut (A_1)\times Aut (sl(2))$ on a particular class of realisations of $sl(2)$ in $A_1$.
Publié le : 2005-04-11
Classification:  Mathematics - Representation Theory,  High Energy Physics - Theory,  Mathematical Physics 
@article{0504224,
     author = {de Traubenberg, M. Rausch and Slupinski, M. J. and Tanasa, A.},
     title = {Finite-dimensional Lie subalgebras of the Weyl algebra},
     journal = {arXiv},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0504224}
}

de Traubenberg, M. Rausch; Slupinski, M. J.; Tanasa, A. Finite-dimensional Lie subalgebras of the Weyl algebra. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0504224/