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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2020
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| Accès en ligne: | https://arxiv.org/abs/2004.10005 |
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| _version_ | 1866917704772878336 |
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| author | Rahaman, Atibur Roy, Sutanu |
| author_facet | Rahaman, Atibur Roy, Sutanu |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2004_10005 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Quantum $E(2)$ groups for complex deformation parameters Rahaman, Atibur Roy, Sutanu Operator Algebras Quantum Algebra 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. |
| title | Quantum $E(2)$ groups for complex deformation parameters |
| topic | Operator Algebras Quantum Algebra |
| url | https://arxiv.org/abs/2004.10005 |