Space of linear differential operators on the real line as a module over the Lie algebra of vector fields
| dc.creator | Gargoubi, H. | |
| dc.creator | Ovsienko, V. | |
| dc.date | 1996-02-04 | |
| dc.date.accessioned | 2026-07-07T09:12:42Z | |
| dc.date.available | 2026-07-07T09:12:42Z | |
| dc.description | Let ${\cal D}^k$ be the space of $k$-th order linear differential operators on ${\bf R}$: $A=a_k(x)\frac{d^k}{dx^k}+\cdots+a_0(x)$. We study a natural 1-parameter family of $\Diff(\bf R)$- (and $\Vect(\bf R)$)-modules on ${\cal D}^k$. (To define this family, one considers arguments of differential operators as tensor-densities of degree $λ$.) In this paper we solve the problem of isomorphism between $\Diff(\bf R)$-module structures on ${\cal D}^k$ corresponding to different values of $λ$. The result is as follows: for $k=3$ $\Diff(\bf R)$-module structures on ${\cal D}^3$ are isomorphic to each other for every values of $λ\not=0,\;1,\;{1\over 2},\;{1\over 2}\pm \frac{\sqrt 21}{6}$, in this case there exists a unique (up to a constant) intertwining operator $T:{\cal D}^3\to{\cal D}^3$. In the higher order case $(k\geq 4)$ $\Diff(\bf R)$-module structures on ${\cal D}^k$ corresponding to two different values of the degree: $λ$ and $λ^{\prime}$, are isomorphic if and only if $λ+λ^{\prime}=1$. | |
| dc.description | 19 pages, anonymous ftp at ftp://cpt.univ-mrs.fr/ or via gopher at gopher://cpt.univ-mrs.fr/ | |
| dc.identifier | https://arxiv.org/abs/dg-ga/9602004 | |
| dc.identifier | http://arxiv.org/abs/dg-ga/9602004 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/152110 | |
| dc.subject | Differential Geometry | |
| dc.title | Space of linear differential operators on the real line as a module over the Lie algebra of vector fields | |
| dc.type | text |