Covariance of a quantum space with respect to a quantum enveloping algebraties the deformation of the multiplication of the space algebra to thedeformation of the coproduct of the enveloping algebra. Since the deformationof the coproduct is governed by a Drinfeld twist, the same twist naturallydefines a covariant star product on the commutative space. However, thisproduct is in general not associative and does not yield the quantum space. Itis shown that there are certain Drinfeld twists which realize the associativeproduct of the quantum plane, quantum Euclidean 4-space, and quantum Minkowskispace. These twists are unique up to a central 2-coboundary. The appropriateformal deformation of real structures of the quantum spaces is also expressedby these twists.
展开▼
