The quantum algebra $U_q(sl_2)$ and its equitable presentation
Ito, Tatsuro ; Terwilliger, Paul ; Weng, Chih-wen
arXiv, 0507477 / Harvested from arXiv
Text on arXiv
We show that the quantum algebra $U_q(sl_2)$ has a presentation with generators $x,x^{-1},y,z$ and relations $x x^{-1}=1$, $x^{-1} x=1$, $\frac{qxy-q^{-1}yx}{q-q^{-1}}=1$, $\frac{qyz-q^{-1}zy}{q-q^{-1}}=1$, $\frac{qzx-q^{-1}xz}{q-q^{-1}}=1$. We call this the equitable presentation. We investigate the action of $x,x^{-1},y,z$ on finite-dimensional $U_q(sl_2)$-modules.
Publié le : 2005-07-22
Classification:  Mathematics - Quantum Algebra,  Mathematical Physics,  17B37 
@article{0507477,
     author = {Ito, Tatsuro and Terwilliger, Paul and Weng, Chih-wen},
     title = {The quantum algebra $U\_q(sl\_2)$ and its equitable presentation},
     journal = {arXiv},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0507477}
}

Ito, Tatsuro; Terwilliger, Paul; Weng, Chih-wen. The quantum algebra $U_q(sl_2)$ and its equitable presentation. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0507477/