国外数学名著系列45(续一 影印版) 代数几何4:线性代数群,不变量理论 [Algebraic Geometry IV: Linear Algebraic Groups, Invariant Theo epub pdf  mobi txt 电子书 下载

国外数学名著系列45(续一 影印版) 代数几何4:线性代数群,不变量理论 [Algebraic Geometry IV: Linear Algebraic Groups, Invariant Theo epub pdf mobi txt 电子书 下载 2024

国外数学名著系列45(续一 影印版) 代数几何4:线性代数群,不变量理论 [Algebraic Geometry IV: Linear Algebraic Groups, Invariant Theo epub pdf mobi txt 电子书 下载 2024


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商品介绍



出版社: 科学出版社有限责任公司
ISBN:9787030234889
版次:1
商品编码:11895595
包装:精装
丛书名: 国外数学名著系列(影印版)
外文名称:Algebraic Geometry IV: Linear Algebraic Groups, Invariant Theory
开本:16开
出版时间:2009-01-01

国外数学名著系列45(续一 影印版) 代数几何4:线性代数群,不变量理论 [Algebraic Geometry IV: Linear Algebraic Groups, Invariant Theo epub pdf mobi txt 电子书 下载 2024



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书籍描述

内容简介

  This book contains two contributions on closely related subjects: the theory of linear algebraic groups and invariant theory. The first part is written by T. A. Springer, a well-known expert in the first mentioned field. Hc presents a comprehensive survey, which contains numerous sketched proofs and he discusses the particular features of algebraic groups over special fields (finite, local, and global). The authors of part two-E. B. Vinbcrg and V. L. Popov-arc among the most active researchers in invariant theory. The last 20 years have bccn a period of vigorous development in this field duc to the influence of modern methods from algebraic geometry.

内页插图

目录

Introduction
Historical Comments

Chapter 1.Linear Algebraic Groups over an Algebraically
1.Recollections from Algebraic Geometry
1.1.Affine Varieties
1.2.Morphisms
1.3.Some Topological Properties
1.4.Tangent Spaces
1.5.Properties of Morphisms
1.6.Non-Affine Varieties
2.Linear Algebraic Groups, Basic Definitions and Properties
2.1.The Definition of a Linear Algebraic Group
2.2.Some Basic Facts
2.3.G-Spaces
2.4.The Lie Algebra of an Algebraic Group
2.5.Quotients
3.Structural Properties of Linear Algebraic Groups
3.1.Jordan Decomposition and Related Results
3.2.Diagonalizable Groups and Tori
3.3.One-Dimensional Connected Groups
3.4.Connected Solvable Groups
3.5.Parabolic Subgroups and Borel Subgroups
3.6.Radicals, Semi-simple and Reductive Groups
4.Reductive Groups
4.1.Groups of Rank One
4.2.The Root Datum and the Root System
4.3.Basic Properties of Reductive Groups
4.4.Existence and Uniqueness Theorems for Reductive Groups
4.5.Classification of Quasi-simple Linear Algebraic Groups
4.6.Representation Theory

Chapter 2.Linear Algebraic Groups over Arbitrary Ground Fields
1.Recollections from Algebraic Geometry
1.1.F-Structures on Affine Varieties
1.2.F-Structures on Arbitrary Varieties
1.3.Forms
1.4.Restriction of the Ground Field
2.F-Groups, Basic Properties
2.1.Generalities About F-Groups
2.2.Quotients
2.3.Forms
2.4.Restriction of the Ground Field
3.Tori
3.1.F-Tori
3.2.F-Tori in F-Groups
3.3.Split Tori in F-Groups
4.Solvable Groups
4.1.Solvable Groups
4.2.Sections
4.3.Elementary Unipotent Groups
4.4.Properties of Split Solvable Groups
4.5.Basic Results About Solvable F-Groups
5.Reductive Groups
5.1.Split Reductive Groups
5.2.Parabolic Subgroups
5.3.The Small Root System
5.4.The Groups G(F)
5.5.The Spherical Tits Building of a Reductive F-Group
6.Classification of Reductive F-Groups
6.1.Isomorphism Theorem
6.2.Existence
6.3.Representation Theory of F-Groups

Chapter 3.Special Fields
1.Lie Algebras of Algebraic Groups in Characteristic Zero
1.1.Algebraic Subalgebras
2.Algebraic Groups and Lie Groups
2.1.Locally Compact Fields
2.2.Real Lie Groups
3.Linear Algebraic Groups over Finite Fields
3.1.Lang's Theorem and its Consequences
3.2.Finite Groups of Lie Type
3.3.Representations of Finite Groups of Lie Type
4.Linear Algebraic Groups over Fields with a Valuation
4.1.The Apartment and Affine Dynkin Diagram
4.2.The Affine Building
4.3.Tits System, Decompositions
4.4.Local Fields
5.Global Fields
5.1.Adele Groups
5.2.Reduction Theory
5.3.Finiteness Results
5.4.Galois Cohomology

References

前言/序言


国外数学名著系列45(续一 影印版) 代数几何4:线性代数群,不变量理论 [Algebraic Geometry IV: Linear Algebraic Groups, Invariant Theo epub pdf mobi txt 电子书 下载 2024

国外数学名著系列45(续一 影印版) 代数几何4:线性代数群,不变量理论 [Algebraic Geometry IV: Linear Algebraic Groups, Invariant Theo 下载 epub mobi pdf txt 电子书 2024

国外数学名著系列45(续一 影印版) 代数几何4:线性代数群,不变量理论 [Algebraic Geometry IV: Linear Algebraic Groups, Invariant Theo pdf 下载 mobi 下载 pub 下载 txt 电子书 下载 2024

国外数学名著系列45(续一 影印版) 代数几何4:线性代数群,不变量理论 [Algebraic Geometry IV: Linear Algebraic Groups, Invariant Theo mobi pdf epub txt 电子书 下载 2024

国外数学名著系列45(续一 影印版) 代数几何4:线性代数群,不变量理论 [Algebraic Geometry IV: Linear Algebraic Groups, Invariant Theo epub pdf mobi txt 电子书 下载
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国外数学名著系列45(续一 影印版) 代数几何4:线性代数群,不变量理论 [Algebraic Geometry IV: Linear Algebraic Groups, Invariant Theo epub pdf mobi txt 电子书 下载 2024

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国外数学名著系列45(续一 影印版) 代数几何4:线性代数群,不变量理论 [Algebraic Geometry IV: Linear Algebraic Groups, Invariant Theo epub pdf mobi txt 电子书 下载 2024


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