Duality for weak multiplier Hopf algebras with sufficiently many integrals

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-10-16 DOI:10.1016/j.aim.2024.109971

Alfons Van Daele , Shuanhong Wang

引用次数: 0

Abstract

We study duality of regular weak multiplier Hopf algebras with sufficiently many integrals. This generalizes the well-known duality of algebraic quantum groups. We need to modify the definition of an integral in this case. It is no longer true that an integral is automatically faithful and unique. Therefore we have to work with a faithful set of integrals. We apply the theory to three cases and give some examples. First we have the two weak multiplier Hopf algebras associated with an infinite groupoid (a small category). Related we answer a question posed by Nicolás Andruskiewitsch about double groupoids. Finally, we also discuss the weak multiplier Hopf algebras associated to a separability idempotent.

查看原文本刊更多论文

具有足够多积分的弱乘数霍普夫数组的对偶性

我们研究具有足够多积分的正则弱乘数霍普夫数组的对偶性。这概括了众所周知的代数量子群的对偶性。在这种情况下，我们需要修改积分的定义。积分自动忠实且唯一的说法不再成立。因此，我们必须使用一组忠实的积分。我们将这一理论应用于三种情况，并给出一些例子。首先是与无限群集（一个小范畴）相关的两个弱乘法霍普夫布拉斯。与此相关，我们回答了尼古拉斯-安德鲁斯基维奇（Nicolás Andruskiewitsch）提出的关于双群的问题。最后，我们还讨论了与可分离幂级数相关的弱乘数霍普夫数组。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.