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

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

2005-07-22

arxiv.org/abs/math/0507477v1

Mathematics

Quantum Algebra

Accepted for publication in J. Algebra

Scientific paper

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.

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