Abstract
We derive necessary conditions on a Lie algebra from the existence of a star product on a neighbourhood of the origin in the dual of the Lie algebra for the coadjoint Poisson structure which is both differential and tangential to all the coadjoint orbits. In particular we show that when the Lie algebra is semisimple there are no differential and tangential star products on any neighbourhood of the origin in the dual of its Lie algebra.
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Communicated by H. Araki
Research partially supported by EC contract CHRX-CT920050
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Cahen, M., Gutt, S. & Rawnsley, J. On tangential star products for the coadjoint Poisson structure. Commun.Math. Phys. 180, 99–108 (1996). https://doi.org/10.1007/BF02101183
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DOI: https://doi.org/10.1007/BF02101183