Realization of q-deformed spacetime as star product by a Drinfeld twist

Abstract

Covariance ties the noncommutative deformation of a space into a quantum space closely to the deformation of the symmetry into a quantum symmetry. Quantum deformations of enveloping algebras are governed by Drinfeld twists, inner automorphisms which relate the deformed to the undeformed coproduct. While Drinfeld twists naturally define a covariant star product on the space algebra, this product is in general not associative and does not yield a quantum space. It is reported that, nevertheless, there are certain Drinfeld twists which realize the quantum plane, quantum Euclidean 4-space, and quantum Minkowski space.

4 pages; LaTeX (uses iopart class); to appear in the proceedings of Group24 (Paris, 2002)

Cited by in corpus (2)

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• Space-Time Diffeomorphisms in Noncommutative Gauge Theories