Star Product and Invariant Integration for Lie type Noncommutative Spacetimes

Abstract

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).

21 pages

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Cited by in corpus (8)

• Voros product, Noncommutative Schwarzschild Black Hole and Corrected Area Law
• Generalized kappa-deformed spaces, star-products, and their realizations
• Star products made (somewhat) easier
• Noncommutative Differential Forms on the kappa-deformed Space
• Classical Mechanics on Noncommutative Space with Lie-algebraic Structure
• Nonassociative Weyl star products
• Lie-Poisson gauge theories and $\kappa$-Minkowski electrodynamics
• Deformed Quantum Phase Spaces, Realizations, Star Products and Twists