English

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

Quantum Algebra 2007-05-23 v1 Mathematical Physics math.MP

Abstract

We consider the quantum group Uq(g)U_q(g) associated with a symmetrizable Kac-Moody algebra gg. We display a presentation for Uq(g)U_q(g) that we find attractive; we call this the equitable presentation. For g=sl2g=sl_2 the equitable presentation has generators X,X1,Y,ZX,X^{-1},Y,Z and relations XX1=1X X^{-1} =1, X1X=1X^{-1} X=1, qXYq1YXqq1=1\frac{qXY-q^{-1}YX}{q-q^{-1}}=1, qYZq1ZYqq1=1\frac{qYZ-q^{-1}ZY}{q-q^{-1}}=1, qZXq1XZqq1=1\frac{qZX-q^{-1}XZ}{q-q^{-1}}=1.

Keywords

Cite

@article{arxiv.math/0507478,
  title  = {The equitable presentation for the quantum group $U_q(g)$ associated with a symmetrizable Kac-Moody algebra $g$},
  author = {Paul Terwilliger},
  journal= {arXiv preprint arXiv:math/0507478},
  year   = {2007}
}

Comments

16 pages. Submitted to J. Algebra