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关键词：
Matrix Groups
- An Introduction to Lie Group Theory
书目信息
ISBN：
9781852334703（13位）
中图分类号：
O1
杜威分类号：
中文译名：
矩阵群：李群理论概论
作者：
Baker
编者：
语种：
English
出版信息
出版社：
Springer
出版地：
出版年：
2003
版本：
1st ed. 2002. Corr. 2nd printing
版本类型：
原版
丛书题名：
Springer Undergraduate Mathematics Series
卷期：
文献信息
关键词：
Mathematics
前言：
摘要：
内容简介：
16Aimed at advanced undergraduate and beginning graduate students, this book provides a first taste of the theory of Lie groups as an appetiser for a more substantial further course. Lie theoretic ideas lie at the heart of much of standard undergraduatelinear algebra and exposure to them can inform or motivate the study of the latter. The main focus is on matrix groups, i.e., closed subgroups of real and complex general linear groups. The first part studies examples and describes the classical f amilies of simply connected compact groups. The second part introduces the idea of a lie group and studies the associated notion of a homogeneous space using orbits of smooth actions. Throughout, the emphasis is on providing an approach that is accessibleto readers equipped with a standard undergraduate toolkit of algebra and analysis. Although the formal prerequisites are kept as low level as possible, the subject matter is sophisticated and contains many of the key themes of the fully deve 16loped theory, preparing students for a more standard and abstract course in Lie theory and differential geometry. 04From the contents:Part I. Basic Ideas and Examples: Real and Complex Matrix Groups. Exponentials, Differential Equations and One Parameter Subgroups. Tangent Spaces and Lie Algebras. Algebras, Quaternions, and Symplectic Groups. Clifford Algebras andSpinor Groups. Lorentz Groups- Part II. Matrix Groups as Lie Groups: Lie groups. Homogeneous Spaces. Connectivity of Matrix Groups- Part III. Compact Connected Lie Groups and their Classification: Maximal Tori in Compact Connected Lie Groups. Semi-simple Factorization. Roots systems, Weyl Groups and Dynkin Diagrams- Bibliography- Index
目次：
Part I Basic ideas and examples: real and complex matrix groups; exponentials, differential equations and one parameter subgroups; tangent spaces and Lie algebras; algebras, quaternions, and symplectic groups; clifford algebras and spinor groups; Lorentz groups. Part II matrix groups as Lie groups: Lie Groups; homogeneous spaces; connectivity of matrix groups; Part III compact connected lie groups and their classification: Maximal tori in compact connected Lie groups; semi-simple factorization; roots systems, Weyl Groups and Dynkin Diagrams.
附录：
全文链接：
读者对象：
undergrad.
实体信息
页码：
装帧：
soft
尺寸：
其它形态细节：
其它信息
原价：
EUR
36.9500
原版ISBN：
其它ISBN：
图书特色：
书评：
扩展信息
Isbn：
1852334703
issue：
2006JC01
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