Cartan connections and natural and projectively equivariant quantizations

Mathonet, Pierre; Radoux, Fabian

doi:10.1112/jlms/jdm030

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Cartan connections and natural and projectively equivariant quantizations

Mathonet, Pierre; Radoux, Fabian

2007 • In Journal of the London Mathematical Society, 76, p. 87-104

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https://hdl.handle.net/2268/88064

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10.1112/jlms/jdm030

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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 :

Pages :

87-104

Peer reviewed :

Peer Reviewed verified by ORBi

Available on ORBi :

since 31 March 2011

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