Derivations of the Lie Algebras of Differential Operators
| dc.creator | Grabowski, J. | |
| dc.creator | Poncin, N. | |
| dc.date | 2003-12-08 | |
| dc.date | 2005-01-17 | |
| dc.date.accessioned | 2026-07-07T06:21:45Z | |
| dc.date.available | 2026-07-07T06:21:45Z | |
| dc.description | This paper encloses a complete and explicit description of the derivations of the Lie algebra D(M) of all linear differential operators of a smooth manifold M, of its Lie subalgebra D^1(M) of all linear first-order differential operators of M, and of the Poisson algebra S(M)=Pol(T*M) of all polynomial functions on T*M, the symbols of the operators in D(M). It turns out that, in terms of the Chevalley cohomology, H^1(D(M),D(M))=H^1_{DR}(M), H^1(D^1(M),D^1(M))=H^1_{DR}(M)\oplus\R^2, and H^1(S(M),S(M))=H^1_{DR}(M)\oplus\R. The problem of distinguishing those derivations that generate one-parameter groups of automorphisms and describing these one-parameter groups is also solved. | |
| dc.description | LaTeX, 15 pages | |
| dc.identifier | https://arxiv.org/abs/math/0312162 | |
| dc.identifier | http://arxiv.org/abs/math/0312162 | |
| dc.identifier | Indag. Mathem., N.S., 16 (2), 181-200, 2005 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/95700 | |
| dc.subject | Differential Geometry | |
| dc.subject | Rings and Algebras | |
| dc.subject | 17B63 (Primary), 13N10, 16S32, 17B40, 17B65, 53D17 (Secondary) | |
| dc.title | Derivations of the Lie Algebras of Differential Operators | |
| dc.type | text |