Author | Seligman, G. B. author |
---|---|
Title | Modular Lie Algebras [electronic resource] / by G. B. Seligman |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1967 |
Connect to | http://dx.doi.org/10.1007/978-3-642-94985-2 |
Descript | X, 166 p. online resource |
I. Fundamentals -- 1. Definitions -- 2. The Poincarรฉ-Birkhoff-Witt theorem -- 3. Free Lie algebras. Restricted Lie algebras -- 4. Iwasawaโs theorem -- 5. Nilpotent Lie algebras. Engelโs theorem -- 6. Cartan subalgebras -- 7. Semisimplicity. The Killing form -- 8. Trace forms, derivations, and restrictedness -- 9. Extension of the base ring -- II. Classical Semisimple Lie Algebras -- 1. The Cartan decomposition -- 2. Split 3-dimensional algebras and applications -- 3. Classical Lie algebras -- 4. Strings of roots and Cartan integers -- 5. Fundamental root systems -- 6. Semisimplicity and simplicity -- 7. Determination of the fundamental systems -- 8. Existence of isomorphisms -- 9. The Weyl group -- 10. Existence of the classical algebras -- 11. Generalizations of the theory -- III. Automorphisms of the Classical Algebras -- 1. The Chevalley groups -- 2. The fundamental decomposition of G. Consequences -- 3. Structure of the Chevalley group -- 4. Conjugacy of Cartan subalgebras -- 5. Structure of the automorphism group -- 6. Realizations -- IV. Forms of the Classical Lie Algebras -- 1. Forms and splitting fields -- 2. Galois semi-automorphisms and 1-cohomology -- 3. Simple involutorial algebras and the types A โ D -- 4. Derivation algebras of alternative and Jordan algebras -- 5. Other types -- 6. Finite fields -- 7. On automorphism groups -- V. Comparison of the Modular and Non-modular Cases -- 1. Solvable and nilpotent algebras -- 2. Representations -- 3. Cohomology -- 4. Known simple Lie algebras -- 5. Derivations -- 6. Extension of the base field -- 7. Cartan subalgebras -- 8. Nilpotent elements and special subalgebras -- VI. Related Topics -- 1. Nilpotent groups and Lie algebras. The restricted Burnside problem -- 2. Linear algebraic groups and Lie algebras -- 3. Formal groups, hyperalgebras and Lie algebras -- 4. Lie derivation algebras and purely inseparable extensions -- 5. Infinite-dimensional analogues of the classical Lie algebras