论文标题
$ u_q（\ widehat {\ mathfrak {sl}} _ 2）$ u_q的正中心扩展的紧凑式演示文稿_ 2）$
A compact presentation for the alternating central extension of the positive part of $U_q(\widehat{\mathfrak{sl}}_2)$
论文作者
论文摘要
本文涉及量子组$ u_q（{\ wideHat {\ mathfrak {sl}}}} _ 2）$ u_q（{\ wideHat {\ wideHat {\ wideHat {\ wideHat）_ 2）的积极部分。代数$ u^+_ q $有一个演示文稿，涉及两个满足立方$ q $ -serre关系的发电机。我们最近引入了一个代数$ \ Mathcal U^+_ Q $，称为$ u^+_ q $的交替中央扩展名。我们通过生成器和关系介绍了$ \ Mathcal U^+_ Q $。演讲很有吸引力，但是众多的发电机和关系使演示文稿变得笨拙。在本文中，我们获得了$ \ Mathcal u^+_ Q $的演示文稿，该介绍涉及原始发电机集的一小部分和非常易于管理的关系集。我们称此演示文稿为$ \ Mathcal U^+_ Q $的紧凑型介绍。
This paper concerns the positive part $U^+_q$ of the quantum group $U_q({\widehat{\mathfrak{sl}}}_2)$. The algebra $U^+_q$ has a presentation involving two generators that satisfy the cubic $q$-Serre relations. We recently introduced an algebra $\mathcal U^+_q$ called the alternating central extension of $U^+_q$. We presented $\mathcal U^+_q$ 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 $\mathcal U^+_q$ 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 $\mathcal U^+_q$.
