16.1 a first approach
　16.2 zariski tangent space
　16.3 differential of a morphism
　16.4 some lemmas
　16.5 smooth points
17 normal varieties
　17.1 normal varieties
　17.2 normalization
　17.3 products of normal varieties
　17.4 properties of normal varieties
18 root systems
　18.1 reflections
　18.2 root systems
　18.3 root systems and bilinear forms
　18.4 passage to the field of real numbers
　18.5 relations between two roots
　18.6 examples of root systems
　18.7 base of a root system
　18.8 weyl chambers
　18.9 highest root
　18.10 closed subsets of roots
　18.11 weights
　18.12 graphs
　18.13 dynkin diagrams
　18.14 classification of root systems
19 lie algebras
　19.1 generalities on lie algebras
　19.2 representations
　19.3 nilpotent lie algebras
　19.4 solvable lie algebras
　19.5 radical and the largest nilpotent ideal
　19.6 nilpotent radical
　19.7 regular linear forms
　19.8 caftan subalgebras
20 semisimple and reductive lie algebras
　20.1 semisimple lie algebras
　20.2 examples
　20.3 semisimplicity of representations
　20.4 semisimple and nilpotent elements
　20.5 reductive lie algebras
　20.6 results on the structure of semisimple lie algebras
　20.7 subalgebras of semisimple lie algebras
　20.8 parabolic subalgebras
21 algebraic groups
　21.1 generalities
　21.2 subgroups and morphisms
　21.3 connectedness
　21.4 actions of an algebraic group
　21.5 modules
　21.6 group closure
22 ailine algebraic groups
　22.1 translations of functions
　22.2 jordan decomposition
　22.3 unipotent groups
　22.4 characters and weights
　22.5 tori and diagonalizable groups
　22.6 groups of dimension one
23 lie algebra of an algebraic group
　23.1 an associative algebra
　23.2 lie algebras
　23.3 examples
　23.4 computing differentials
　23.5 adjoint representation
　23.6 jordan decomposition
24 correspondence between groups and lie algebras
　24.1 notations
　24.2 an algebraic subgroup
　24.3 invariants
　24.4 functorial properties
　24.5 algebraic lie subalgebras
　24.6 a particular case
　24.7 examples
　24.8 algebraic adjoint group
25 homogeneous spaces and quotients
　25.1 homogeneous spaces
　25.2 some remarks
　25.3 geometric quotients
　25.4 quotient by a subgroup
　25.5 the case of finite groups
26 solvable groups
　26.1 conjugacy classes
　26.2 actions of diagonalizable groups
　26.3 fixed points
　26.4 properties of solvable groups
　26.5 structure of solvable groups
27 reductive groups
　27.1 radical and unipotent radical
　27.2 semisimple and reductive groups
　27.3 representations
　27.4 finiteness properties
　27.5 algebraic quotients
　27.6 characters
28 borel subgroups, parabolic subgroups, cartan subgroups
　28.1 borel subgroups
　28.2 theorems of density
　28.3 centralizers and tori
　28.4 properties of parabolic subgroups
　28.5 cartan subgroups
29 cartan subalgebras, borel subalgebras and parabolic
　subalgebras
　29.1 generalities
　29.2 cartan subalgebras
　29.3 applications to semisimple lie algebras
　29.4 borel subalgebras
　29.5 properties of parabolic subalgebras
　29.6 more on reductive lie algebras
　29.7 other applications
　29.8 maximal subalgebras
30 representations of semisimple lie algebras
　 30.1 enveloping algebra
　 30.2 weights and primitive elements
　 30.3 finite-dimensional modules
　 30.4 verma modules
　 30.5 results on existence and uniqueness
　 30.6 a property of the weyl group
31 symmetric invariants
　 31.1 invariants of finite groups
　 31.2 invariant polynomial functions
　 31.3 a free module
32 s-triples
　32.1 jacobson-morosov theorem
　32.2 some lemmas
　32.3 conjugation of s-triples
　32.4 characteristic
　32.5 regular and principal elements
33 polarizations
　33.1 definition of polarizations
　33.2 polarizations in the semisimple case
　33.3 a non-polarizable element
　33.4 polarizable elements
　33.5 richardson's theorem
34 results on orbits
　34.1 notations
　34.2 some lemmas
　34.3 generalities on orbits
　34.4 minimal nilpotent orbit
　34.5 subregular nilpotent orbit
　34.6 dimension of nilpotent orbits
　34.7 prehomogeneous spaces of parabolic type
35 centralizers
　35.1 distinguished elements
　35.2 distinguished parabolic subalgebras
　35.3 double centralizers
　35.4 normalizers
　35.5 a semisimple lie subalgebra
　35.6 centralizers and regular elements

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