Quantum E(2) groups for complex deformation parameters

Abstract

We construct a family of q deformations of E(2) group for nonzero complex parameters |q| 1 as locally compact braided quantum groups over the circle group viewed as a quasitriangular quantum group with respect to the unitary R-matrix R(m,n):= (q/q)mn for all m,n. For real 0 |q| 1, the deformation coincides with Woronowicz's Eq(2) groups. As an application, we study the braided analogue of the contraction procedure between SUq(2) and Eq(2) groups in the spirit of Woronowicz's quantum analogue of the classic Ino;diedie-Wigner group contraction. Consequently, we obtain the bosonization of braided Eq(2) groups by contracting Uq(2) groups. ;copy 2021 World Scientific Publishing Company.