Exceptional Lie Algebras

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.

Introduction 1. Jordan algebras of symmetric bilinear forms 2. Cayley algebras 3. Exceptional Jordan algebras 4. Automorphisms of 5. Exceptional Lie algebras of type D4 6. Roots of and 6 7. Lie algebras of type E6 8. Some applications of Galois cohomology 9. Lie algebras of type E7 10. Tits' second construction 11. Calculation of the Killing forms 12. Models of the real forms