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

Paul M. Terwilliger

Abstract


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+.


Keywords


q-Onsager algebra, q-Serre relations, q-shuffle algebra, tridiagonal pair

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DOI: https://doi.org/10.26493/1855-3974.2669.58c

ISSN: 1855-3974

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