The equitable presentation for the quantum group $U_q(g)$ associated with a symmetrizable Kac-Moody algebra $g$

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dc.creatorTerwilliger, Paul
dc.date2005-07-22
dc.date.accessioned2026-07-07T05:21:56Z
dc.date.available2026-07-07T05:21:56Z
dc.descriptionWe consider the quantum group $U_q(g)$ associated with a symmetrizable Kac-Moody algebra $g$. We display a presentation for $U_q(g)$ that we find attractive; we call this the equitable presentation. For $g=sl_2$ the equitable presentation has generators $X,X^{-1},Y,Z$ and relations $X X^{-1} =1$, $X^{-1} X=1$, $\frac{qXY-q^{-1}YX}{q-q^{-1}}=1$, $\frac{qYZ-q^{-1}ZY}{q-q^{-1}}=1$, $\frac{qZX-q^{-1}XZ}{q-q^{-1}}=1$.
dc.description16 pages. Submitted to J. Algebra
dc.identifierhttps://arxiv.org/abs/math/0507478
dc.identifierhttp://arxiv.org/abs/math/0507478
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/75877
dc.subjectQuantum Algebra
dc.subjectMathematical Physics
dc.subject17B37
dc.titleThe equitable presentation for the quantum group $U_q(g)$ associated with a symmetrizable Kac-Moody algebra $g$
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