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Title: Traces for star products on the dual of a Lie algebra
Authors: Bieliavsky, P ×
Gutt, S
Bordemann, M
Waldmann, Stefan #
Issue Date: Jul-2003
Publisher: World Scientific
Series Title: Reviews in Mathematical Physics vol:15 issue:5 pages:425-445
Abstract: 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.
URI: 
ISSN: 0129-055X
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Geometry Section
× corresponding author
# (joint) last author

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