Three Hopf algebras from number theory, physics & topology, and their common background I: operadic & simplicial aspects

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2016-07-01 DOI:10.4310/cntp.2020.v14.n1.a1

Imma G'alvez-Carrillo, R. Kaufmann, A. Tonks

引用次数: 8

Abstract

We consider three a priori totally different setups for Hopf algebras from number theory, mathematical physics and algebraic topology. These are the Hopf algebra of Goncharov for multiple zeta values, that of Connes-Kreimer for renormalization, and a Hopf algebra constructed by Baues to study double loop spaces. We show that these examples can be successively unified by considering simplicial objects, co-operads with multiplication and Feynman categories at the ultimate level. These considerations open the door to new constructions and reinterpretations of known constructions in a large common framework, which is presented step-by-step with examples throughout. In this first part of two papers, we concentrate on the simplicial and operadic aspects.

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来自数论、物理和拓扑学的三个Hopf代数及其共同背景I:操作和简单方面

我们从数论、数学物理和代数拓扑三个方面先验地考虑了Hopf代数的三种完全不同的设置。这些是Goncharov的多重zeta值的Hopf代数，cones - kreimer的重整化的Hopf代数，以及Baues构造的研究双环空间的Hopf代数。我们证明了这些例子可以通过考虑简单对象，与乘法和费曼范畴在最终水平上的合作来连续统一。这些考虑为在一个大的公共框架中使用新结构和对已知结构的重新解释打开了大门，该框架通过示例逐步呈现。在这两篇论文的第一部分，我们集中在简单和操作两个方面。

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

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.