The quantum algebra U_q(sl₂) and its equitable presentation

2005/07/22 by Tatsuro Ito, Paul Terwilliger, Ito, Tatsuro +3
Mathematics · Physics and Astronomy · #17B37 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #math-ph #math.MP #math.QA #msc:17B37

paper · pdf · doi:10.48550/arxiv.math/0507477

Accepted for publication in J. Algebra

arxiv created 2005/07/22 · arxiv updated 2009/12/01

Abstract

We show that the quantum algebra U_q(sl₂) has a presentation with generators x,x^-1,y,z and relations x x^-1=1, x^-1 x=1, \fracqxy-q^-1yxq-q^-1=1, \fracqyz-q^-1zyq-q^-1=1, \fracqzx-q^-1xzq-q^-1=1. We call this the equitable presentation. We investigate the action of x,x^-1,y,z on finite-dimensional U_q(sl₂)-modules.

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