The contraction of $S{U}_{\mu }(2)$ 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 $S{U}_{\mu }(2)$. 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}.

30 pages Latex file