Star Product and Invariant Integration for Lie type Noncommutative Spacetimes

Details Star Product and Invariant Integration for Lie type Noncommutative Spacetimes Star Product and Invariant Integration for Lie type Noncommutative Spacetimes

2007-05-25

arxiv.org/abs/0705.3780v1

JHEP 0708:012,2007

Physics

High Energy Physics

High Energy Physics - Theory

21 pages

Scientific paper

10.1088/1126-6708/2007/08/012

We present a star product for noncommutative spaces of Lie type, including the so called ``canonical'' case by introducing a central generator, which is compatible with translations and admits a simple, manageable definition of an invariant integral. A quasi-cyclicity property for the latter is shown to hold, which reduces to exact cyclicity when the adjoint representation of the underlying Lie algebra is traceless. Several explicit examples illuminate the formalism, dealing with kappa-Minkowski spacetime and the Heisenberg algebra (``canonical'' noncommutative 2-plane).

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