Geodesic
Finite-dimensional Lie Subalgebras of the Weyl Algebra
Journal of Lie theory, Tome 16 (2006) no. 3, pp. 427-454 Cet article a éte moissonné depuis la source Heldermann Verlag

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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 countable and, for example, the only non-solvable Lie algebras with this property are: $\frak{sl}(2)$, $\frak{sl}(2)\times{\bf C}$ and $\frak{sl}(2)\ltimes{\cal H}_3$. We then give several different characterisations, normal forms and isotropy groups for the action of ${\rm Aut}(A_1)\times {\rm Aut}(\frak{sl}(2))$ on a class of realisations of $\frak{sl}(2)$ in $A_1$.
Classification : 16S32, 17B60
Mots-clés : Finite-dimensional Lie subalgebras, Weyl algebra, embeddings 
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     author = {M. Rausch de Traubenberg and M. J. Slupinski and A. Tanasa },
     title = {Finite-dimensional {Lie} {Subalgebras} of the {Weyl} {Algebra}},
     journal = {Journal of Lie theory},
     pages = {427--454},
     year = {2006},
     volume = {16},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/JLT_2006_16_3_JLT_2006_16_3_a1/}
}
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M. Rausch de Traubenberg; M. J. Slupinski; A. Tanasa . Finite-dimensional Lie Subalgebras of the Weyl Algebra. Journal of Lie theory, Tome 16 (2006) no. 3, pp. 427-454. http://geodesic.mathdoc.fr/item/JLT_2006_16_3_JLT_2006_16_3_a1/