A compact presentation for the alternating central extension of the positive part of Uq(sl^2)

Abstract

This paper concerns the positive part U_q⁺ of the quantum group U_q(sl^{^}₂). The algebra U_q⁺ has a presentation involving two generators that satisfy the cubic q-Serre relations. We recently introduced an algebra U_q⁺ called the alternating central extension of U_q⁺. We presented U_q⁺ by generators and relations. The presentation is attractive, but the multitude of generators and relations makes the presentation unwieldy. In this paper we obtain a presentation of U_q⁺ that involves a small subset of the original set of generators and a very manageable set of relations. We call this presentation the compact presentation of U_q⁺.