Article (Scientific journals)
Cartan connections and natural and projectively equivariant quantizations
Mathonet, Pierre; Radoux, Fabian
2007In Journal of the London Mathematical Society, 76, p. 87-104
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Keywords :
Quantization; Cartan connections; Projective structures
Abstract :
[en] In this paper, the question of existence of a natural and projectively equivariant symbol calculus is analysed using the theory of projective Cartan connections. A close relationship is established between the existence of such a natural symbol calculus and the existence of an sl(m+1,R)-equivariant calculus over R^m . Moreover, it is shown that the formulae that hold in the non-critical situations over R^m for the sl(m+1,R)-equivariant calculus can be directly generalized to an arbitrary manifold by simply replacing the partial derivatives by invariant differentiations with respect to a Cartan connection.
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 :
Cartan connections and natural and projectively equivariant quantizations
Publication date :
2007
Journal title :
Journal of the London Mathematical Society
ISSN :
0024-6107
eISSN :
1469-7750
Publisher :
Oxford University Press, United Kingdom
Volume :
76
Pages :
87-104
Peer reviewed :
Peer Reviewed verified by ORBi
Available on ORBi :
since 31 March 2011

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