代数群和微分Galois理论（影印版）
￥99.00定价
作者： Teresa Crespo，Zbigniew Hajto
出版时间：2019-01
出版社：高等教育出版社
- 高等教育出版社
- 9787040510133
- 1版
- 239160
- 45245978-7
- 精装
- 16开
- 2019-01
- 248
- 248
- 理学
- 数学
- 数学类
- 研究生（硕士、EMBA、MBA、MPA、博士）
内容简介
微分Galois理论在最近的数十年中已经成为诸多方向上的研究热点。本书是自封闭的，通过展示Picard-Vessiot理论，即线性偏微分方程的Galois理论，将读者带入主题。书中的第一部分和第二部分给出了所需的代数几何和代数群的先导知识，第三部分包括Picard-Vessiot扩张、Picard-Vessiot理论的基本定理、求积法的可解性、Fuchs方程、单值群和Kovacic算法。书中的100多道习题可以帮助读者深入理解相关的概念并扩展了部分主题。
本书可作为研究生的微分Galois理论课程的教学参考书。最后一章中包含的扩展阅读的若干建议激励读者进入微分Galois理论或相关领域的更深入的不同主题。
目录
PrefaceIntroductionPart 1． Algebraic GeometryChapter 1．Affine and Projective Varieties1．1．Affine varieties1．2．Abstract affine varieties1．3．Projective varietiesExercisesChapter 2．Algebraic Varieties2．1．Prevarieties2．2．VarietiesExercisesPart 2． Algebraic GroupsChapter 3．Basic Notions3．1．The notion of Mgebraic group3．2．Connected algebraic groups3．3．Subgroups and morphisms3．4．Linearization of affine algebraic groups3．5．Homogeneous spaces3．6．Characters and semi-invariants3．7．QuotientsExercisesChapter 4．Lie Algebras and Algebraic Groups4．1．Lie algebras4．2．The Lie algebra of a linear algebraic group4．3．Decomposition of algebraic groups4．4．Solvable algebraic groups4．5．Correspondence between algebraic groups and Lie algebras4．6．Subgroups of SL（2， C）ExercisesPart 3． Differential Galois TheoryChapter 5．Picard-Vessiot Extensions5．1．Derivations5．2．Differential rings5．3．Differential extensions5．4．The ring of differential operators5．5．Homogeneous linear differential equations5．6．The Picard-Vessiot extensionExercisesChapter 6．The Galois Correspondence6．1．Differential Galois group6．2．The differential Galois group as a linear algebraic group6．3．The fundamental theorem of differential Galois theory6．4．Liouville extensions6．5．Generalized Liouville extensionsExercisesChapter 7．Differential Equations over C（z）7．1．Fuchsian differential equations7．2．Monodromy group7．3．Kovacic's algorithmExercisesChapter 8．Suggestions for Further ReadingBibliographyIndex
