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

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

2005-07-22

arxiv.org/abs/math/0507478v1

Mathematics

Quantum Algebra

16 pages. Submitted to J. Algebra

Scientific paper

We 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 $X X^{-1} =1$, $X^{-1} X=1$, $\frac{qXY-q^{-1}YX}{q-q^{-1}}=1$, $\frac{qYZ-q^{-1}ZY}{q-q^{-1}}=1$, $\frac{qZX-q^{-1}XZ}{q-q^{-1}}=1$.

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