Classical Groups: Course Given in Spring Term 1965 at Yale University |
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algebra analogous anti-automorphism argument assume automorphism char characteristic space characterized clearly commutator subgroup conjugate define denote dimension dimensional division ring duality e₁ elements Euclidian extreme involutions fixed follows form a minimal GL₂ hence hermitian form homomorphism hyperbolic plane hyperplane implies induces intersection invariant isomorphism isotropic line isotropic point isotropic vectors kernel leaves Lemma Let G linear space linear transformation lines containing mapping matrix maximal totally isotropic minimal couple Moreover n-dimensional non-commutative non-degenerate nonisotropic lines nonisotropic vector normal subgroup orthogonal group P₁ permutation group projective proof of 5.2 prove quasi-reflection reflection result rotation s-linear singular skew hermitian SL(K SL₂ F3 structure suppose T₁ T₂ totally isotropic subspace trace valued transvections Tx,a U₁ U₂ unitary transvections V₁ W₁ W₂ Witt's Theorem XA-x α α λεκ