论文标题
量子$ e（2）$组的复杂变形参数
Quantum $E(2)$ groups for complex deformation parameters
论文作者
论文摘要
我们构建了一个$ q $的家庭$ e（2）$组成的非零复数参数的$ | q | <1 $作为圆圈组$ \ mathbb {t} $在局部紧凑的编织量子组，被视为quasitriangular量子量子组，与单位r-matrix $ r（M-r-matrix $ r（for All） $ m，n \ in \ mathbb {z} $。对于真正的$ 0 <| q | <1 $，变形与woronowicz的$ e_ {q}（2）$组相吻合。作为应用程序，我们研究了$ su_ {q}（2）$和$ e_ {q}（2）$组之间的收缩过程的编织类似物，本着沃罗诺维奇经典的inönünününününim-wigner群的量子类似物的精神。因此，我们通过收缩$ u_ {q}（2）$组来获得编织的$ e_ {q}（2）$组的效率。
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 $\mathbb{T}$ viewed as a quasitriangular quantum group with respect to the unitary R-matrix $R(m,n):=(ζ)^{mn}$ for all $m,n\in\mathbb{Z}$. For real $0<|q|<1$, the deformation coincides with Woronowicz's $E_{q}(2)$ groups. As an application, we study the braided analogue of the contraction procedure between $SU_{q}(2)$ and $E_{q}(2)$ groups in the spirit of Woronowicz's quantum analogue of the classic Inönü-Wigner group contraction. Consequently, we obtain the bosonisation of braided $E_{q}(2)$ groups by contracting $U_{q}(2)$ groups.
