The contraction of $SU_\mu(2)$ and its differential structures to $E_\kappa(2)$

Abstract

The deformed double covering of E(2) group, denoted by $\tilde{E}_\kappa(2)$, is obtained by contraction from the $SU_\mu(2)$. The contraction procedure is then used for producing a new examples of differential calculi: 3D-left covariant calculus on both $\tilde{E}_\kappa(2)$ and the deformed Euclidean group $E_\kappa(2)$ and two different 4D-bicovariant calculi on $\tilde{E}_\kappa(2)$ which correspond to the one 4D-bicovariant calculi on $E_\kappa(2)$ described in Ref.\cite{b14}.