QUANTUM SU(2) AND E(2) GROUPS - CONTRACTION PROCEDURE

In [3] it was shown (in the framework of deformed enveloping algebras) that quantum SU(2) and E(2) groups are related by the contraction procedure. We consider the same problem on the C*-level. As a result we find a number of formulae coupling the comultiplications in quantum SU(2) and E(2). In particular we show that the comultiplications in both groups are implemented by partial isometries. An unexpected feature of quantum E(2) is discovered and the corresponding strange behavior of quantum SU(2) is described.