Lectures on Algebraic Groups: Fall Term 1966-1967, Yale University |
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1817 LIBRARIES abelian action affine algebraic k-set algebraic extension algebraic group defined algebraic k-set algebraic set defined assume Aut k/k automorphisms bijective CHIGAN closed subgroup closed subset commutative contains defined over K Definition denote dense diagram dim G dimensional direct product elements equivalence of categories exists exponent finite fixed points function system G defined galois extension galois group group G group scheme homomorphism isomorphic k-algebra k-characters k-closed k-closure k-connected k-dense k-open subset k-free k-group k-homomorphism k-irreducible k-isomorphism k-locally closed k-morphism k-open affine k-rational k-regular k-split k-torus k-wound kernel Lemma Let G linearly disjoint mapping morphism Mult non-trivial non-zero open sets polynomial pre-algebraic k-set prescheme Proof Proposition purely inseparable regular functions resp rings semi-simple solvable group structure subgroup of G Suppose Theorem topology torus defined unipotent group unique UNIVE UNIVERSITY V₁ vector group defined vector space X₁