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Projectively and conformally invariant star-products

C. Duval·A. M. El Gradechi·V. Ovsienko
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Abstract

We consider the Poisson algebra S(M) of smooth functions on T^*M which are fiberwise polynomial. In the case where M is locally projectively (resp. conformally) flat, we seek the star-products on S(M) which are SL(n+1,R) (resp. SO(p+1,q+1))-invariant. We prove the existence of such star-products using the projectively (resp. conformally) equivariant quantization, then prove their uniqueness, and study their main properties. We finally give an explicit formula for the canonical projectively invariant star-product.

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BibTeXRIS

C. Duval, A. M. El Gradechi, V. Ovsienko. 2003-02-17. Projectively and conformally invariant star-products. https://doi.org/10.1007/s00220-003-0973-7

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