2002/09/15 by Christian Blohmann · 2 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Noncommutative and Quantum Gravity Theories #hep-th #math.QA #msc:17B37 #msc:81R60
paper · pdf · doi:10.1063/1.1602553
published as J.Math.Phys. 44 (2003) 4736-4755
arxiv created 2002/09/15 · openalex publication_date 2003/09/25 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Covariance of a quantum space with respect to a quantum enveloping algebra ties the deformation of the multiplication of the space algebra to the deformation of the coproduct of the enveloping algebra. Since the deformation of the coproduct is governed by a Drinfeld twist, the same twist naturally defines a covariant star product on the commutative space. However, this product is in general not associative and does not yield the quantum space. It is shown that there are certain Drinfeld twists which realize the associative product of the quantum plane, quantum Euclidean four-space, and quantum Minkowski space. These twists are unique up to a central two-coboundary. The appropriate formal deformation of real structures of the quantum spaces is also expressed by these twists.