Koszul operads governing props and wheeled props

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-08-05 DOI:10.1016/j.aim.2024.109869

Kurt Stoeckl

引用次数: 0

Abstract

In this paper, we construct groupoid coloured operads governing props and wheeled props, and show they are Koszul. This is accomplished by new biased definitions for (wheeled) props, and an extension of the theory of Groebner bases for operads to apply to groupoid coloured operads. Using the Koszul machine, we define homotopy (wheeled) props, and show they are not formed by polytope based models. Finally, using homotopy transfer theory, we construct Massey products for (wheeled) props, show these products characterise the formality of these structures, and re-obtain a theorem of Mac Lane on the existence of higher homotopies of (co)commutative Hopf algebras.

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管理螺旋桨和轮式螺旋桨的 Koszul 操作板

在本文中，我们构建了支配道具和轮状道具的类群彩色操作数，并证明它们是科斯祖尔的。这是通过对（轮状）道具的新偏置定义，以及将操作数的格罗伯纳基数理论扩展到类群彩色操作数来实现的。利用科斯祖尔机器，我们定义了同构（轮状）道具，并证明它们不是由基于多面体的模型形成的。最后，利用同构转移理论，我们构建了（轮）道具的马西乘积，证明这些乘积是这些结构的形式特征，并重新获得了麦克-莱恩关于（共）交换霍普夫代数的高同构存在性的定理。

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.