1st Edition

Exceptional Lie Algebras

By N. Jacobson Copyright 1971
    136 Pages
    by CRC Press

    136 Pages
    by CRC Press

    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.



    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



    N. Jacobson