线性代数群-第2版_PDF下载[123MB-百度云]斯普林格

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《线性代数群(第2版)(英文版)》由世界图书出版公司北京公司出版。

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本书特色

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　　this volume is a completely new version of the book under the same title， which appeared in 1981 as volume 9 in the series “progress in mathematics，” and which has been out of print for some time. that book had its origin in notes （taken by hassan azad） from a course on the theory of linear algebraic groups， given at the university of notre dame in the fall of 1978. the aim of the book was to present the theory of linear algebraic groups over an algebraically closed field， including the basic results on reductive groups. a distinguishing feature was a self-contained treatment of the prerequisites from algebraic geometry and commutative algebra.

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preface to the second edition 1. some algebraic geometry 1.1. the zariski topology 1.2. lrreducibility of topological spaces 1.3. affine algebras 1.4. regular functions, ringed spaces1.5. products1.6. prevarieties and varieties 1.7. projective varieties1.8. dimension1.9. some results on morphisms notes 2. linear algebraic groups, first properties2.1. algebraic groups 2.2. some basic results 2.3. g-spaces2.4. jordan decomposition2.5. recovering a group from its representationsnotes 3. commutative algebraic groups3.1. structure of commutative algebraic groups 3.2. diagonalizable groups and tori 3.3. additive functions3.4. elementary unipotent groupsnotes 4. demrations, differntials, lie algebras4.1. derivations and tangent spaces4.2. differentials, separability4.3. simple points4.4. the lie algebra of a linear algebraic groupnotes5. topological properties of morphisms, applications5.1. topological properties of morphisms5.2. fjnite morphisms, normality5.3. homogeneous spaces5.4. semi-simple automorphisms5.5. quotientsnotes6. parabolic subgroups, borel subgoups solvable groups6.1. complete varieties6.2. parabolic subgroups and borcl subgroups6.3. connected solvable groups6.4. maximal tori, further properties of borel groupsnotes7. weyl group, roots, root datum8. reductive groups9. the isomorphism theorem10. the existence theorem11. more algebraic geometry12. f-groups: general results13. f-tori14. solvable f-groups15. f_reductive groups16. redoctive f-groups17. classificationtable of indicesbibliographyindex