元胞群的估值、补全和双曲作用

IF 16.4 1区 化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2024-05-23 DOI:10.1112/jlms.12916
Carolyn R. Abbott, Sahana Balasubramanya, Alexander J. Rasmussen
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引用次数: 0

摘要

双曲度量空间上的作用是研究群的重要工具,因此,尝试对固定群的所有此类作用进行分类是很自然的,但也很困难。在本文中,我们在双曲几何和交换代数之间建立了强有力的联系,以便对众多元胞群的共界双曲作用进行分类,直至粗等价。特别是,我们将这一分类问题转化为对某些环的完备性中的理想进行分类以及计算矩阵的不变子空间的问题。我们利用这个框架对许多与扩展整数矩阵相关的无旁系逐周期群的共界双曲作用进行了分类。每个这样的作用都等价于对树或海因策群(一类经典研究的负弯李群)的作用。我们的研究包括数系统、形式幂级数环中的因式分解、补全和估值。
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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Valuations, completions, and hyperbolic actions of metabelian groups

Actions on hyperbolic metric spaces are an important tool for studying groups, and so it is natural, but difficult, to attempt to classify all such actions of a fixed group. In this paper, we build strong connections between hyperbolic geometry and commutative algebra in order to classify the cobounded hyperbolic actions of numerous metabelian groups up to a coarse equivalence. In particular, we turn this classification problem into the problems of classifying ideals in the completions of certain rings and calculating invariant subspaces of matrices. We use this framework to classify the cobounded hyperbolic actions of many abelian-by-cyclic groups associated to expanding integer matrices. Each such action is equivalent to an action on a tree or on a Heintze group (a classically studied class of negatively curved Lie groups). Our investigations incorporate number systems, factorization in formal power series rings, completions, and valuations.

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来源期刊
Accounts of Chemical Research
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.
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