Comodules of $U_q(sl_2)$ and modules of $SL_q(2)$ via quiver
| dc.creator | Chen, Xiao-Wu | |
| dc.creator | Zhang, Pu | |
| dc.date | 2004-09-09 | |
| dc.date | 2004-12-28 | |
| dc.date.accessioned | 2026-07-07T12:53:16Z | |
| dc.date.available | 2026-07-07T12:53:16Z | |
| dc.description | The aim of this paper is to construct comodules of $U_q(sl_2)$ and modules of $SL_q(2)$ via quiver, where $q$ is not a root of unity. By embedding the quantized algebra $U_q(sl_2)$ into the path coalgebra $k\mathcal{D}^c$, where $\mathcal{D}$ is the Gabriel quiver of $U_q(sl_2)$ as a coalgebra, we obtain a basis of $U_q(sl_2)$ in terms of combinations of paths in the quiver $\mathcal{D}$; this special basis enable us to describe the category of $U_q(sl_2)$-comodules by certain representations of $\mathcal{D}$; and this description further permits us to construct a class of modules of the quantum special linear group $SL_q(2)$, from certain representations of $\mathcal{D}$, via the duality between $U_q(sl_2)$ and $SL_q(2)$. | |
| dc.description | 19 pages | |
| dc.identifier | https://arxiv.org/abs/math/0409159 | |
| dc.identifier | http://arxiv.org/abs/math/0409159 | |
| dc.identifier | Journal of Pure and Applied Algebra, 211(3) (2007), 862-876 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/223564 | |
| dc.subject | Quantum Algebra | |
| dc.title | Comodules of $U_q(sl_2)$ and modules of $SL_q(2)$ via quiver | |
| dc.type | text |