Algebraic and Differential Star Products on Regular Orbits of Compact Lie Groups

Details Algebraic and Differential Star Products on Regular Orbits of Compact Lie Groups Algebraic and Differential Star Products on Regular Orbits of Compact Lie Groups

2000-11-22

arxiv.org/abs/math/0011172v2

Pacific J.Math. 206 (2002) 321-337

Mathematics

Quantum Algebra

AMS-LaTeX, 20 pages. Version to appear in the Pacific Journal of Mathematics

Scientific paper

In this paper we study a family of algebraic deformations of regular coadjoint orbits of compact semisimple Lie groups with the Kirillov Poisson bracket. The deformations are restrictions of deformations on the dual of the Lie algebra. We prove that there are non isomorphic deformations in the family. The star products are not differential, unlike the star products considered in other approaches. We make a comparison with the differential star product canonically defined by Kontsevich's map.

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