Overview

In 1925 Elie Cartan introduced the principal of triality specifically for the Lie groups of type $D_4$, and in 1935 Ruth Moufang initiated the study of Moufang loops. The observation of the title in 1978 was made by Stephen Doro, who was in turn motivated by the work of George Glauberman from 1968. Here the author makes 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.''

Full Product Details

Author:   J.I. Hall
Publisher:   American Mathematical Society
Imprint:   American Mathematical Society
Weight:   0.297kg
ISBN:  

9781470436223

ISBN 10:   1470436221
Pages:   188
Publication Date:   30 October 2019
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

Part 1. Basics: Category theory Quasigroups and loops Latin square designs Groups with triality Part 2. Equivalence: The functor ${\mathbf {B}}$ Monics, covers, and isogeny in $\mathsf {TriGrp}$ Universals and adjoints Moufang loops and groups with triality are essentially the same thing Moufang loops and groups with triality are not exactly the same thing Part 3. Related Topics: The functors ${\mathbf {S}}$ and ${\mathbf {M}}$ The functor ${\mathbf {G}}$ Multiplication groups and autotopisms Doro's approach Normal Structure Some related categories and objects Part 4. Classical Triality: An introduction to concrete triality Orthogonal spaces and groups Study's and Cartan's triality Composition algebras Freudenthal's triality The loop of units in an octonion algebra Bibliography Index.

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J. I. Hall, Michigan State University, East Lansing.

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