Finite-dimensional Lie subalgebras of the Weyl algebra

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dc.creatorde Traubenberg, M. Rausch
dc.creatorSlupinski, M. J.
dc.creatorTanasa, A.
dc.date2005-04-11
dc.date2005-06-14
dc.date.accessioned2026-07-07T06:24:54Z
dc.date.available2026-07-07T06:24:54Z
dc.descriptionWe 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 $A_1$.
dc.descriptionLatex 27 pages; some proofs are given with more details
dc.identifierhttps://arxiv.org/abs/math/0504224
dc.identifierhttp://arxiv.org/abs/math/0504224
dc.identifierJ. Lie Theory 16 (2006) 427-454
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/96699
dc.subjectRepresentation Theory
dc.subjectHigh Energy Physics - Theory
dc.subjectMathematical Physics
dc.titleFinite-dimensional Lie subalgebras of the Weyl algebra
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