2004/02/12 by Christian Blohmann, Blohmann, Christian
Mathematics · Physics and Astronomy · #17B37 #81R60 #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum Algebra (math.QA) #hep-th #math.QA #msc:17B37 #msc:81R60
paper · pdf · doi:10.48550/arxiv.math/0402199
4 pages; LaTeX (uses iopart class); to appear in the proceedings of Group24 (Paris, 2002)
arxiv created 2004/02/12 · arxiv updated 2009/12/01
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.