1992/10/08 by Majid, Shahn · 1 citation
#FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum Algebra (math.QA)
paper · doi:10.48550/arxiv.hep-th/9210044
We introduce *-structures on braided groups and braided matrices. Using this, we show that the quantum double D(Uq(su2)) can be viewed as the quantum algebra of observables of a quantum particle moving on a hyperboloid in q-Minkowski space (a three-sphere in the Lorentz metric), and with the role of angular momentum played by Uq(su2). This provides a new example of a quantum system whose algebra of observables is a Hopf algebra. Furthermore, its dual Hopf algebra can also be viewed as a quantum algebra of observables, of another quantum system. This time the position space is a q-deformation of SL(2,\R) and the momentum group is Uq(su2^*) where su2^* is the Drinfeld dual Lie algebra of su2. Similar results hold for the quantum double and its dual of a general quantum group.