On quantization of quadratic Poisson structures

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.

Submitted to Comm. Math. Phys. Version 2 : error in introduction corrected