Lie Algebras and Algebraic Groups

- Preface
- Results on topological spaces
- Rings and modules
- Integral extensions
- Factorial rings
- Field extensions
- Finitely generated algebras
- Gradings and filtrations
- Inductive limits
- Sheaves of functions
- Jordan decomposition and some basic results on groups
- Algebraic sets
- Prevarieties and varieties
- Projective varieties
- Dimension
- Morphisms and dimension
- Tangent spaces
- Normal varieties
- Root systems
- Lie algebras
- Semisimple and reductive Lie algebras
- Algebraic groups
- Affine algebraic groups
- Lie algebra of an algebraic group
- Correspondence between groups and Lie algebras
- Homogeneous spaces and quotients
- Solvable groups
- Reductive groups
- Borel subgroups, parabolic subgroups and Cartan subgroups
- Cartan subalgebras, Borel subalgebras and parabolic subalgebras
- Representations of semisimple Lie algebras
- Symmetric invariants
- S-triples
- Polarizations
- Results on orbits
- Centralizers
- S -root systems
- Symmetric Lie algebras
- Semisimple symmetric Lie algebras
- Sheets of Lie algebras
- Index and linear forms
- References
- Index of notations
- Index of terminologies.