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Modular Lie Algebras

The study of the structure of Lie algebras over arbitrary fields is now a little more than thirty years old. The first papers, to my know­ ledge, which undertook this study as an end in itself were those of JACOBSON (" Rational methods in the theory of Lie algebras ") in the Annals, and of...

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Bibliographic Details
Main Author: Seligman, Geoge B.
Format: eBook
Language:English
Published: Berlin, Heidelberg Springer Berlin Heidelberg 1967, 1967
Edition:1st ed. 1967
Series:Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge, A Series of Modern Surveys in Mathematics
Subjects:
Topological Groups And Lie Groups
Lie Groups
Topological Groups
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • I. Fundamentals
  • 1. Definitions
  • 2. The Poincaré-Birkhoff-Witt theorem
  • 3. Free Lie algebras. Restricted Lie algebras
  • 4. Iwasawa’s theorem
  • 5. Nilpotent Lie algebras. Engel’s 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 — 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 Liealgebras
  • 4. Lie derivation algebras and purely inseparable extensions
  • 5. Infinite-dimensional analogues of the classical Lie algebras

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