The contraction of SU mu(2) and its differential structures to E-kappa(2)

The deformed double covering of the E(2) group, denoted by (E) over tilde(k appa)(2), is obtained by contraction from the SUmu(2). The contraction proc edure is then used for producing new examples of differential calculi: thre e-dimensional left covariant calculus on both (E) over tilde(kappa)(2) and the deformed Euclidean group E-kappa(2) and two different four-dimensional (4D)-bicovariant calculi on (E) over tilde(kappa)(2) which correspond to th e one 4D-bicovariant calculi on E-kappa(2) described by Giller [Acta Phys. Pol. B 28, 1121 (1997)]. (C) 2000 American Institute of Physics. [S0022- 24 88(00)01505-X].