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

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 + .