The equitable presentation for the quantum group Uq(g)Uq(g) associated with a symmetrizable Kac–Moody algebra gg

We consider the quantum group Uq(g)Uq(g) associated with a symmetrizable Kac–Moody algebra gg. We display a presentation for Uq(g)Uq(g) that we find attractive; we call this the equitable   presentation. For g=sl2g=sl2 the equitable presentation has generators X±1,Y,ZX±1,Y,Z and relations XX−1=X−1X=1XX−1=X−1X=1,qXY−q−1YXq−q−1=1,qYZ−q−1ZYq−q−1=1,qZX−q−1XZq−q−1=1.