《代數群和微分Galois 理論》是2019年高等教育出版社出版的圖書，作者是Teresa，Crespo，Zbigniew，Hajto。
基本介紹
- 書名：代數群和微分Galois 理論
- 作者：Teresa，Crespo，Zbigniew，Hajto
- 出版社：高等教育出版社
- ISBN：9787040510133
內容簡介,圖書目錄,
內容簡介
微分Galois理論在最近的數十年中已經成為諸多方向上的研究熱點。
《代數群和微分Galois理論（影印版 英文版）》是自封閉的，通過展示Picard-Vessiot理論，即線性偏微分方程的Galois理論，將讀者帶入主題。
《代數群和微分Galois理論（影印版 英文版）》中的第一部分和第二部分給出了所需的代數幾何和代數群的先導知識，第三部分包括Picard-Vessiot擴張、Picard-Vessiot理論的基本定理、求積法的可解性、Fuchs方程、單值群和Kovacic算法。書中的100多道習題可以幫助讀者深入理解相關的概念並擴展了部分主題。
《代數群和微分Galois理論（影印版 英文版）》可作為研究生的微分Galois理論課程的教學參考書。最後一章中包含的擴展閱讀的若干建議激勵讀者進入微分Galois理論或相關領域的更深入的不同主題。
圖書目錄
Preface
Introduction
Part 1． Algebraic Geometry
Chapter 1．Affine and Projective Varieties
1．1．Affine varieties
1．2．Abstract affine varieties
1．3．Projective varieties
Exercises
Chapter 2．Algebraic Varieties
2．1．Prevarieties
2．2．Varieties
Exercises
Part 2． Algebraic Groups
Chapter 3．Basic Notions
3．1．The notion of Mgebraic group
3．2．Connected algebraic groups
3．3．Subgroups and morphisms
3．4．Linearization of affine algebraic groups
3．5．Homogeneous spaces
3．6．Characters and semi-invariants
3．7．Quotients
Exercises
Chapter 4．Lie Algebras and Algebraic Groups
4．1．Lie algebras
4．2．The Lie algebra of a linear algebraic group
4．3．Decomposition of algebraic groups
4．4．Solvable algebraic groups
4．5．Correspondence between algebraic groups and Lie algebras
4．6．Subgroups of SL（2， C）
Exercises
Part 3． Differential Galois Theory
Chapter 5．Picard-Vessiot Extensions
5．1．Derivations
5．2．Differential rings
5．3．Differential extensions
5．4．The ring of differential operators
5．5．Homogeneous linear differential equations
5．6．The Picard-Vessiot extension
Exercises
Chapter 6．The Galois Correspondence
6．1．Differential Galois group
6．2．The differential Galois group as a linear algebraic group
6．3．The fundamental theorem of differential Galois theory
6．4．Liouville extensions
6．5．Generalized Liouville extensions
Exercises
Chapter 7．Differential Equations over C（z）
7．1．Fuchsian differential equations
7．2．Monodromy group
7．3．Kovacic's algorithmExercises
Chapter 8．Suggestions for Further Reading
Bibliography
Index
