Збережено в:
| Автори: | , |
|---|---|
| Формат: | Preprint |
| Опубліковано: |
2020
|
| Предмети: | |
| Онлайн доступ: | https://arxiv.org/abs/2004.10005 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
Зміст:
- 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.