Keyword: theorem

Theorem Affine Finite-Type Groups Have Faithful Finite-Dimensional Representations admitted

Theorem Affine G-Varieties Embed Equivariantly in Representations admitted

Theorem Algebra Homomorphisms Form a Group Under Convolution admitted

Theorem Antipode of a Commutative Hopf Algebra Is Multiplicative admitted

Theorem Antipode of a Hopf Algebra Is Anti-Multiplicative admitted

Theorem Base Change Preserves Algebraic Group Structure admitted

Theorem Borel Fixed Point Theorem 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

Theorem Characterization of Diagonalizable Groups admitted

Theorem Characters Are Group-Like Elements admitted

Theorem Chevalley Existence Theorem admitted

Theorem Chevalley Isomorphism Theorem admitted

Theorem Chevalley Isomorphism Theorem for F-Split Groups admitted

Theorem Classification of Rank-One Tori admitted

Theorem Commutative Algebraic Groups Split into Semisimple and Unipotent Parts admitted

Theorem Composition with the Antipode Is an Algebra Hom for Commutative Hopf Algebras admitted

Theorem Connected Subgroups Generate a Closed Connected Subgroup admitted

Theorem Convolution Is Pointwise Multiplication admitted

Theorem Convolution of Algebra Homomorphisms Is an Algebra Homomorphism admitted

Theorem Diagonalizable Groups Are Dual to Character Groups admitted

Theorem Embedding Theorem for Algebraic Groups admitted

Theorem Essential Image of Spec Is Affine Group Schemes admitted

Theorem F-Tori Are Classified by Galois Modules admitted

Theorem Field of Definition for Subgroups of F-Groups admitted

Theorem Finiteness of Tori of Bounded Rank admitted

Theorem Fixed Point Theorem for F-Split Solvable Groups admitted

Theorem G-Representations Are A-Comodules admitted

Theorem Galois Descent for Hopf Algebras admitted

Theorem Group Object Structure on Spec A via Yoneda admitted

Theorem Hom Into Spec via Global Sections (Spec ⊣ Γ Adjunction) admitted

Theorem Homomorphisms of Tori Correspond to Lattice Maps admitted

Theorem Identity Component Is Closed Normal of Finite Index admitted

Theorem Image of an Algebraic Group Homomorphism Is Closed admitted

Theorem Jordan Decomposition in a Linear Algebraic Group admitted

Theorem Lang Theorem for Connected Algebraic Groups over Finite Fields admitted

Theorem Levi Decomposition for Parabolic F-Subgroups admitted

Theorem Levi Decomposition of Parabolic Subgroups 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

Theorem Maximal Tori Are Conjugate admitted

Theorem Orbits of Algebraic Group Actions Are Locally Closed admitted

Theorem Points of GL_n Are Invertible n×n Matrices over R admitted

Theorem Points of 𝔾_a Are the Additive Group of R admitted

Theorem Points of 𝔾_m Are the Units of R admitted

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

Theorem Quotient by a Closed Subgroup Exists admitted

Theorem R-Points of a Group Scheme Form a Group admitted

Theorem Radical and Derived Group of a Reductive Group admitted

Theorem Rational Bruhat Decomposition admitted

Theorem Relative Root Datum of an F-Reductive Group admitted

Theorem Relative Weyl Group Is Generated by Relative Reflections admitted

Theorem Resolution of a Torus by Induced Tori admitted

Theorem Root Subgroups Generate a Reductive Group admitted

Theorem Spec Functor on Hopf Algebras Is Fully Faithful admitted

Theorem Split-Anisotropic Decomposition of a Torus admitted

Theorem Standard Parabolics Are Classified by Simple Roots admitted

Theorem Structure of Connected Solvable Algebraic Groups admitted

Theorem Subtori and Quotients via the Character Lattice admitted

Theorem The Minimal Splitting Field of a Torus admitted

Theorem Tori Are Classified by Cocycles in GL_n(Z) admitted

Theorem Tori among Groups of Multiplicative Type admitted

Theorem Tori up to Isogeny Are Rational Representations admitted

Theorem Unipotent Subgroups Are Triangularizable admitted

Theorem Weil Restriction of Tori admitted

Theorem Weyl Group Is Generated by Root Reflections admitted