作者：斯普林格
页数：334
出版社：世界图书出版公司
出版日期：2013
ISBN：9787510058103
电子书格式：pdf/epub/txt
内容简介
本书的第一版讲述了代数封闭域上的线性代数群表示理论，这是第二版，做了全面的修订，扩充，将此理论扩充到任意域上，即不一定需要代数封闭。本书在理论上也上了一个层次，但风格上和第一版保持一致，自成体系，将所需的代数几何和交换代数部分，以及基本约化群基本知识囊括其中。因此，本书的第一部分是线性代数群初学者的是不容错过的。目次：代数几何基础；线性代数群，第一性质；交换代数群；导数、微分和李群；态射的拓扑性质；抛物子群，Borel子群和可解群；Weyl群，根和基准根；约化群；同态定理；存在定理；更多代数几何；F-tori；可解F群；F约化群；约化F群；类。
作者简介
T. A. Springer是国际知名学者，在数学和物理学界享有盛誉。本书凝聚了作者多年科研和教学成果，适用于科研工作者、高校教师和研究生。
本书特色
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.
目录
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 spaces
1.5. products
1.6. prevarieties and varieties
1.7. projective varieties
1.8. dimension
1.9. some results on morphisms
notes
2. linear algebraic groups, first properties
2.1. algebraic groups
2.2. some basic results
2.3. g-spaces
2.4. jordan decomposition
2.5. recovering a group from its representations
notes
3. commutative algebraic groups
3.1. structure of commutative algebraic groups
3.2. diagonalizable groups and tori
3.3. additive functions
3.4. elementary unipotent groups
notes
4. demrations, differntials, lie algebras
4.1. derivations and tangent spaces
4.2. differentials, separability
4.3. simple points
4.4. the lie algebra of a linear algebraic group
notes
5. topological properties of morphisms, applications
5.1. topological properties of morphisms
5.2. fjnite morphisms, normality
5.3. homogeneous spaces
5.4. semi-simple automorphisms
5.5. quotients
notes
6. parabolic subgroups, borel subgoups solvable groups
6.1. complete varieties
6.2. parabolic subgroups and borcl subgroups
6.3. connected solvable groups
6.4. maximal tori, further properties of borel groups
notes
7. weyl group, roots, root datum
8. reductive groups
9. the isomorphism theorem
10. the existence theorem
11. more algebraic geometry
12. f-groups: general results
13. f-tori
14. solvable f-groups
15. f_reductive groups
16. redoctive f-groups
17. classification
table of indices
bibliography
index
节选
《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。
