Projectively equivariant symbol calculus
| dc.creator | Lecomte, P. B. A. | |
| dc.creator | Ovsienko, V. Yu. | |
| dc.date | 1998-09-11 | |
| dc.date.accessioned | 2026-07-07T05:25:58Z | |
| dc.date.available | 2026-07-07T05:25:58Z | |
| dc.description | The spaces of linear differential operators on ${\mathbb{R}}^n$ acting on tensor densities of degree $λ$ and the space of functions on $T^*{\mathbb{R}}^n$ which are polynomial on the fibers are not isomorphic as modules over the Lie algebra $\Vect({\mathbb{R}}^n)$ of vector fields on ${\mathbb{R}}^n$. However, these modules are isomorphic as $sl(n+1,{\mathbb{R}})$-modules where $sl(n+1,{\mathbb{R}})\subset \Vect({\mathbb{R}}^n)$ is the Lie algebra of infinitesimal projective transformations. In addition, such an $sl_{n+1}$-equivariant bijection is unique (up to normalization). This leads to a notion of projectively equivariant quantization and symbol calculus for a manifold endowed with a (flat) projective structure. We apply the $sl_{n+1}$-equivariant symbol map to study the $\Vect(M)$-modules of linear differential operators acting on tensor densities, for an arbitrary manifold $M$. | |
| dc.description | 23 pages, LaTeX This article is a revised version of the electronic preprint dg-ga/9611006 | |
| dc.identifier | https://arxiv.org/abs/math/9809061 | |
| dc.identifier | http://arxiv.org/abs/math/9809061 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/77385 | |
| dc.subject | Differential Geometry | |
| dc.subject | Quantum Algebra | |
| dc.title | Projectively equivariant symbol calculus | |
| dc.type | text |