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The quantum algebra $U_q(sl_2)$ and its equitable presentation | | Tatsuro Ito
; Paul Terwilliger
; Chih-wen Weng
; | | Date: |
22 Jul 2005 | | Subject: | Quantum Algebra; Mathematical Physics MSC-class: 17B37 | math.QA math-ph math.MP | | Abstract: | 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. | | Source: | arXiv, math.QA/0507477 | | Services: | Forum | Review | PDF | Favorites | |
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