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On quantization of quadratic Poisson structures

D. Manchon·M. Masmoudi·A. Roux
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Abstract

Any classical r-matrix on the Lie algebra of linear operators on a real vector space V gives rise to a quadratic Poisson structure on V which admits a deformation quantization stemming from the construction of V. Drinfel'd. We exhibit in this article an example of quadratic Poisson structure which does not arise this way.

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D. Manchon, M. Masmoudi, A. Roux. 2001-05-28. On quantization of quadratic Poisson structures. https://doi.org/10.1007/s002201000575

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