Exceptional Lie Algebras  book cover
1st Edition

Exceptional Lie Algebras





ISBN 9780824713263
Published June 1, 1971 by CRC Press
136 Pages

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Book Description

This volume presents a set of models for the exceptional Lie algebras over algebraically closed fieldsof characteristic O and over the field of real numbers. The models given are based on the algebras ofCayley numbers (octonions) and on exceptional Jordan algebras. They are also valid forcharacteristics p * 2. The book also provides an introduction to the problem of forms of exceptionalsimple Lie algebras, especially the exceptional D4 's, � 6 's, and � 7 's. These are studied by means ofconcrete realizations of the automorphism groups.Exceptional Lie Algebras is a useful tool for the mathematical public in general-especially thoseinterested in the classification of Lie algebras or groups-and for theoretical physicists.

Table of Contents

Preface

Introduction

Jordan algebras of symmetric bilinear forms

Cayley algebras

Exceptional Jordan algebras

Automorphisms of D4’s

Exceptional Lie algebras of type D4

Roots of F4 and E6

Lie algebras of type E6

Some applications of Galois cohomology

Lie algebras of type E7

Tits’ second construction

Calculation of the Killing forms

Models of the real forms

Bibliography

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