Mathematics – Representation Theory
Scientific paper
2005-04-11
J. Lie Theory 16 (2006) 427-454
Mathematics
Representation Theory
Latex 27 pages; some proofs are given with more details
Scientific paper
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 $A_1$.
de Traubenberg Michel Rausch
Slupinski M. J.
Tanasa Adrian
No associations
LandOfFree
Finite-dimensional Lie subalgebras of the Weyl algebra does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Finite-dimensional Lie subalgebras of the Weyl algebra, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Finite-dimensional Lie subalgebras of the Weyl algebra will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-21484