Reference : Cartan connections and natural and projectively equivariant quantizations
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/2268/88064
Cartan connections and natural and projectively equivariant quantizations
English
Mathonet, Pierre mailto [Université de Liège - ULiège > Département de mathématique > Département de mathématique >]
Radoux, Fabian mailto [Université de Liège - ULiège > Département de mathématique > Géométrie et théorie des algorithmes >]
2007
Journal of the London Mathematical Society
76
87-104
Yes (verified by ORBi)
International
0024-6107
1469-7750
[en] Quantization ; Cartan connections ; Projective structures
[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.
Researchers
http://hdl.handle.net/2268/88064
also: http://hdl.handle.net/2268/92212
10.1112/jlms/jdm030

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