Algebraic and differential star products on regular orbits of compact Lie groups

R. Fioresi, A. Levrero and M.A. Lledó

Vol. 206 (2002), No. 2, 321–337

DOI: 10.2140/pjm.2002.206.321

Abstract

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.

Milestones

Received: 4 December 2000

Revised: 9 April 2001

Published: 1 October 2002