Skip Navigation



Journal of the London Mathematical Society Advance Access published online on June 12, 2009
Journal of the London Mathematical Society, doi:10.1112/jlms/jdp024
This Article
Right arrow FREE Full Text (PDF) Freely available
Right arrow All Versions of this Article:
80/1/256    most recent
jdp024v1
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Mathonet, P.
Right arrow Articles by Radoux, F.
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© 2009 London Mathematical Society

On natural and conformally equivariant quantizations

P. Mathonet and F. Radoux

Department of Mathematics
University of Liège
Grande Traverse, 12 - B37
B-4000 Liège
Belgium
Fabian.Radoux@ulg.ac.be

The concept of conformally equivariant quantization was introduced by C. Duval, P. Lecomte and V. Ovsienko for manifolds endowed with flat conformal structures. They obtained results of existence and uniqueness (up to normalization) of such a quantization procedure. A natural generalization of this concept is to seek for a quantization procedure, over a manifold M, that depends on a pseudo-Riemannian metric, is natural and is invariant with respect to a conformal change of the metric. The existence of such a procedure was conjectured by P. Lecomte and proved by C. Duval and V. Ovsienko for symbols of degree at most 2 and by S. Loubon Djounga for symbols of degree 3. In two recent papers, we investigated the question of existence of projectively equivariant quantizations using the framework of Cartan connections. Here we shall show how the formalism developed in these works adapts in order to deal with the conformally equivariant quantization for symbols of degree at most 3. This will allow us to easily recover the results of C. Duval, V. Ovsienko and S. Loubon Djounga. We shall then show how it can be modified in order to prove the existence of conformally equivariant quantizations for symbols of degree 4.

2000 Mathematics Subject Classification 53A30, 53C10.

F. Radoux was partially supported by the Ministère de la Culture, de l’Enseignement supérieur et de la Recherche of the Grand Duchy of Luxembourg (BFR 06/077).

Received June 29, 2007; revised January 29, 2009;
Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer: Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.