Geodesic
A compact presentation for the alternating central extension of the positive part of Uq(sl^2)
Ars Mathematica Contemporanea, Tome 22 (2022) no. 3, article no. 01, 24 p.

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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+.
DOI : 10.26493/1855-3974.2669.58c
Keywords: q-Onsager algebra, q-Serre relations, q-shuffle algebra, tridiagonal pair 
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Paul M. Terwilliger. A compact presentation for the alternating central extension of the positive part of Uq(sl^2). Ars Mathematica Contemporanea, Tome 22 (2022) no. 3, article  no. 01, 24 p. doi : 10.26493/1855-3974.2669.58c. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.2669.58c/

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