Article (Scientific journals)
On natural and conformally invariant quantizations
Mathonet, Pierre; Radoux, Fabian
2009In Journal of the London Mathematical Society, 80 (1), p. 256-272
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Keywords :
Natural and conformally equivariant quantizations,; Cartan connections; Conformal connections
Abstract :
[en] The concept of conformally equivariant quantization was introduced by Duval, Lecomte and 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 will 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 earlier results on the subject. We will then show how it can be modified in order to prove the existence of conformally equivariant quantizations for symbols of degree 4.
Disciplines :
Mathematics
Author, co-author :
Mathonet, Pierre ;  Université de Liège - ULiège > Département de mathématique > Département de mathématique
Radoux, Fabian ;  Université de Liège - ULiège > Département de mathématique > Géométrie et théorie des algorithmes
Language :
English
Title :
On natural and conformally invariant quantizations
Publication date :
2009
Journal title :
Journal of the London Mathematical Society
ISSN :
0024-6107
eISSN :
1469-7750
Publisher :
Oxford University Press, United Kingdom
Volume :
80
Issue :
1
Pages :
256-272
Peer reviewed :
Peer Reviewed verified by ORBi
Available on ORBi :
since 01 April 2011

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