Moufang Loops and Groups with Triality are Essentially the Same Thing

IF 2 4区数学 Q1 MATHEMATICS

Memoirs of the American Mathematical Society Pub Date : 2019-07-01 DOI:10.1090/MEMO/1252

J. Hall

引用次数: 7

Abstract

In 1925 Elie Cartan introduced the principal of triality specifically for the Lie groups of type D4, and in 1935 Ruth Moufang initiated the study of Moufang loops. The observation of the title was made by Stephen Doro in 1978 who was in turn motivated by work of George Glauberman from 1968. Here we make the statement precise in a categorical context. In fact the most obvious categories of Moufang loops and groups with triality are not equivalent, hence the need for the word “essentially.” Received by the editor 20 June 2016. 2010 Mathematics Subject Classification. Primary 20.

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具有三角性的模方圈和群本质上是一回事

1925年Elie Cartan专门为D4型李群引入了三重性原理，1935年Ruth Moufang开始了Moufang环路的研究。这个标题是Stephen Doro在1978年提出的，他受到了George Glauberman在1968年的研究的启发。在这里，我们在直言的上下文中使这个陈述变得精确。事实上，最明显的“某方圈”和“具有审判性的群”的范畴是不等同的，因此需要“本质”一词。2016年6月20日收稿。2010年数学学科分类。20主。

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

Memoirs of the American Mathematical Society 数学-数学

CiteScore

3.50

自引率

5.30%

发文量

审稿时长

>12 weeks

期刊介绍： Memoirs of the American Mathematical Society is devoted to the publication of research in all areas of pure and applied mathematics. The Memoirs is designed particularly to publish long papers or groups of cognate papers in book form, and is under the supervision of the Editorial Committee of the AMS journal Transactions of the AMS. To be accepted by the editorial board, manuscripts must be correct, new, and significant. Further, they must be well written and of interest to a substantial number of mathematicians.