## Lectures on Chevalley groups, Parts 1-4 |

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### Contents

Simplicity of G | 47 |

Chevalley groups and algebraic groups | 56 |

Generators and relations | 66 |

8 other sections not shown

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### Common terms and phrases

Abelian algebraic group algebraically closed Assume basis center of G central extension Chevalley group choose coefficients commutes conjugate Corollary corresponding defined denote diagonal double cosets elements equation Exercise exists finite field fixed follows G is universal group G Hence homomorphism indecomposable induction integral invariant isomorphism KG-module lattice Lemma Lemma 32 Let G LIBRARIES STANFORD UNIVERSITY Lie algebra Lie group linear matrices maximal minimal expression multiplication nonzero normal subgroup orthogonal permutation polynomial positive roots proof of Theorem prove relations Remark result root system semisimple semisimple Lie algebra simple roots STANFORD UNIVERSITY STANFORD UNIVERSITY LIBRARIES subgroup of G subset superdiagonal t e k Theorem 24 unipotent UNIVERSITY LIBRARIES STANFORD vector space Weyl group whence write x e G xa(t