Quantum \(SU(2)\) and \(E(2)\) groups. Contraction procedure (Q1201417)

The author shows how the contraction procedure works in the theory of topological quantum groups. He considers the problem that quantum \(SU(2)\) and \(E(2)\) groups are related by contraction procedure on the \(C^*\)- level. In particular, he finds a number of formulae relating the comultiplications in quantum \(SU(2)\) and \(E(2)\) groups, and shows that the comultiplications in both groups are implemented by partial isometries. In addition, the author discovers an unexpected feature of quantum \(E(2)\) and describes the corresponding strange behavior of quantum \(SU(2)\). It turns out that in certain aspects they behave like locally compact semigroups.