Algebraic Groups.Reductive Groups

Theorem Borel Fixed Point Theorem admitted

Topic Borel Subgroups admitted

Theorem Borel Subgroups Are Conjugate and Control Parabolics admitted

Theorem Bruhat Decomposition admitted

Theorem Bruhat Order Gives Schubert Closure Relations admitted

Theorem Cartan Subgroups from Maximal Tori admitted

Topic Central Isogenies admitted

Theorem Characterization of Diagonalizable Groups admitted

Theorem Chevalley Existence Theorem admitted

Definition Chevalley Group Construction from a Root Datum admitted

Theorem Chevalley Isomorphism Theorem admitted

Theorem Chevalley Isomorphism Theorem for F-Split Groups admitted

Theorem Commutative Algebraic Groups Split into Semisimple and Unipotent Parts admitted

Topic Derived Group, Center, Adjoint Group, and Simply Connected Cover admitted

Topic Diagonalizable Groups admitted

Theorem Diagonalizable Groups Are Dual to Character Groups admitted

Theorem Fixed Point Theorem for F-Split Solvable Groups admitted

Definition Indexed Root Datum of an F-Reductive Group admitted

Definition Isogeny Types from the Root Datum admitted

Theorem Jordan Decomposition in Algebraic Groups admitted

Theorem Levi Decomposition for Parabolic F-Subgroups admitted

Theorem Levi Decomposition of Parabolic Subgroups admitted

Topic Levi Subgroups and Unipotent Radicals admitted

Theorem Lie-Kolchin Theorem admitted

Theorem Maximal F-Split Tori Are G(F)-Conjugate admitted

Theorem Maximal F-Tori Exist in Connected F-Groups admitted

Topic Maximal Tori admitted

Theorem Maximal Tori Are Conjugate admitted

Topic Parabolic Subgroups admitted

Theorem Quasi-Split and Anisotropic Groups via the Indexed Root Datum admitted

Theorem Radical and Derived Group of a Reductive Group admitted

Definition Rank-One Subgroups and SL₂-Embeddings admitted

Theorem Rational Bruhat Decomposition admitted

Topic Reductive Groups admitted

Theorem Relative Root Datum of an F-Reductive Group admitted

Theorem Relative Weyl Group Is Generated by Relative Reflections admitted

Definition Root Datum of a Reductive Group admitted

Theorem Root Subgroups Generate a Reductive Group admitted

Definition Semisimple Conjugacy Classes admitted

Topic Semisimple Groups admitted

Topic Solvable Groups admitted

Definition Split Reductive Groups admitted

Theorem Standard Parabolics Are Classified by Simple Roots admitted

Theorem Structure of Connected Solvable Algebraic Groups admitted

Definition Unipotent Elements and the Unipotent Variety admitted

Topic Unipotent Groups admitted

Theorem Unipotent Radical of a Borel Subgroup and Positive Roots admitted

Theorem Unipotent Subgroups Are Triangularizable admitted

Theorem Weyl Group Is Generated by Root Reflections admitted