par Bieliavsky, Pierre 
;Bordemann, Martin ;Gutt, Simone ;Waldmann, Stefan
Référence Reviews in mathematical physics, 15, 5, page (425-445)
Publication Publié, 2003
;Bordemann, Martin ;Gutt, Simone ;Waldmann, Stefan Référence Reviews in mathematical physics, 15, 5, page (425-445)
Publication Publié, 2003
Article révisé par les pairs
| Résumé : | In this paper, we describe all traces for the BCH star-product on the dual of a Lie algebra. First we show by an elementary argument that the BCH as well as the Kontsevich star-product are strongly closed if and only if the Lie algebra is unimodular. In a next step we show that the traces of the BCH star-product are given by the ad-invariant functionals. Particular examples are the integration over coadjoint orbits. We show that for a compact Lie group and a regular orbit one can even achieve that this integration becomes a positive trace functional. In this case we explicitly describe the corresponding GNS representation. Finally we discuss how invariant deformations on a group can be used to induce deformations of spaces where the group acts on. |
