The quantum algebra $U_q(sl_2)$ and its equitable presentation

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dc.creatorIto, Tatsuro
dc.creatorTerwilliger, Paul
dc.creatorWeng, Chih-wen
dc.date2005-07-22
dc.date.accessioned2026-07-07T05:21:56Z
dc.date.available2026-07-07T05:21:56Z
dc.descriptionWe 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.
dc.descriptionAccepted for publication in J. Algebra
dc.identifierhttps://arxiv.org/abs/math/0507477
dc.identifierhttp://arxiv.org/abs/math/0507477
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/75876
dc.subjectQuantum Algebra
dc.subjectMathematical Physics
dc.subject17B37
dc.titleThe quantum algebra $U_q(sl_2)$ and its equitable presentation
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