PBW bases for ıquantum groups

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra Pub Date : 2025-07-28 DOI:10.1016/j.jalgebra.2025.07.014

Ming Lu , Ruiqi Yang , Weinan Zhang

引用次数: 0

Abstract

We establish PBW type bases for ıquantum groups of arbitrary finite type, using the relative braid group symmetries. Explicit formulas for root vectors are provided for ıquantum groups of each rank 1 type. We show that our PBW type bases give rise to integral bases for the modified ıquantum groups. The leading terms of our bases can be identified with the usual PBW bases in the theory of quantum groups.

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ıquantum基团的PBW碱基

利用相对编织群对称性，建立了任意有限型ıquantum群的PBW型基。为每个等级为1的ıquantum组提供了根向量的显式公式。我们发现我们的PBW型碱基产生了修饰ıquantum基团的整碱基。我们的碱基的主要项可以与量子群理论中常用的PBW碱基相识别。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Algebra 数学-数学

CiteScore

1.50

自引率

22.20%

发文量

414

审稿时长

2-4 weeks

期刊介绍： The Journal of Algebra is a leading international journal and publishes papers that demonstrate high quality research results in algebra and related computational aspects. Only the very best and most interesting papers are to be considered for publication in the journal. With this in mind, it is important that the contribution offer a substantial result that will have a lasting effect upon the field. The journal also seeks work that presents innovative techniques that offer promising results for future research.