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

Christian Blohmann
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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.

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Christian Blohmann. 2004-02-12. Realization of q-deformed spacetime as star product by a Drinfeld twist. https://arxiv.org/abs/math/0402199

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