Cartan Connections and Natural and Projectively Equivariant Quantizations
نویسنده
چکیده
In this paper, we analyse the question of existence of a natural and projectively equivariant symbol calculus, using the theory of projective Cartan connections. We establish a close relationship between the existence of such a natural symbol calculus and the existence of an sl(m+1,R)equivariant calculus over R in the sense of [15, 1]. Moreover we show that the formulae that hold in the non-critical situation over R 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.
منابع مشابه
Natural and Projectively Equivariant Quantizations by Means of Cartan Connections
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