# The algebra $U^+_q$ and its alternating central extension $\mathcal U^+_q$

@inproceedings{Terwilliger2021TheA, title={The algebra \$U^+\_q\$ and its alternating central extension \$\mathcal U^+\_q\$}, author={Paul M. Terwilliger}, year={2021} }

Let U+ q denote the positive part of the quantized enveloping algebra Uq(ŝl2). The algebra U+ q has a presentation involving two generators W0, W1 and two relations, called the q-Serre relations. In 1993 I. Damiani obtained a PBW basis for U+ q , consisting of some elements {Enδ+α0} ∞ n=0, {Enδ+α1} ∞ n=0, {Enδ} ∞ n=1. In 2019 we introduced the alternating central extension U+ q of U + q . We defined U + q by generators and relations. The generators, said to be alternating, are denoted {W−k} ∞ k…

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