Projectively and Conformally Invariant Star-Products |
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| Authors: | C?Duval AM El?Gradechi Email author" target="_blank">V?OvsienkoEmail author |
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| Institution: | (1) Université de la Méditerranée and CPT-CNRS, Luminy Case 907, 13288 Marseille, Cedex 9, France;(2) Faculté des Sciences, Université d Artois, 62307 Lens, France;(3) CPT-CNRS, Luminy Case 907, 13288 Marseille, Cedex 9, France;(4) Institut Girard Desargues, Université Claude Bernard Lyon 1, 69622 Villeubanne, Cedex, France |
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| Abstract: | We consider the Poisson algebra S(M) of smooth functions on T
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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, ) (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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