Moufang loops and groups with triality are essentially the same thing / J.I. Hall.

Format:

Book

Author/Creator:

Hall, J. I., author.

Series:

Memoirs of the American Mathematical Society ; no. 1252.

Memoirs of the American Mathematical Society, 0065-9266 ; number 1252

Language:

English

Subjects (All):

Moufang loops.

Physical Description:

1 online resource (206 pages) : illustrations.

Edition:

1st ed.

Place of Publication:

Providence, RI : American Mathematical Society, [2019]

Summary:

"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.""-- Provided by publisher.

Contents:

Category theory

Quasigroups and loops

Latin square designs

Groups with triality

The functor B

Monics, covers, and isogeny in 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

The functors S and M

The functor G

Multiplication groups and autotopisms

Doro's approach

Normal structure

Some related categories and objects

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.

Notes:

"July 2019, volume 260, number 1252 (third of 5 numbers)."

Description based on online resource; title from PDF title page (ebrary, viewed October 15, 2019).

Includes bibliographical references and index.

ISBN:

1-4704-5321-5