Lectures on Algebraic Groups, Volume 1 |
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abelian affine algebraic k-set algebraic group defined algebraically closed assume Aut k/k automorphisms bijective closed subgroup closed subset commutative group composition series connected solvable connected unipotent contains Corollary defined over K Definition denote dense diagram dim G direct product exists f₁ field fixed point follows function system G defined galois extension galois group group G group scheme homomorphism induction hypothesis irreducible isomorphic k-algebra K-characters k-closed k-connected k-dense k-free k-group k-homomorphism k-irreducible k-isomorphism k-locally closed k-morphism k-open subset k-rational k-regular k-split k-torus k-wound k₁ kernel Lemma Let f Let G linearly disjoint mapping morphism Mult noetherian non-trivial normal open sets polynomial pre-algebraic pre-algebraic k-set prescheme Proof Proposition regular functions resp semi-simple solvable group Spec subgroup of G Suppose Theorem topological space topology tori torus defined U₁ unipotent group unique V₁ vector group defined vector space X₁