A compact presentation for the alternating central extension of the positive part of Uq(sl^2)
Keywords:q-Onsager algebra, q-Serre relations, q-shuffle algebra, tridiagonal pair
This paper concerns the positive part Uq+ of the quantum group Uq(sl^2). The algebra Uq+ has a presentation involving two generators that satisfy the cubic q-Serre relations. We recently introduced an algebra Uq+ called the alternating central extension of Uq+. We presented Uq+ 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 Uq+ 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 Uq+.
Articles in this journal are published under Creative Commons Attribution 4.0 International License