Matrix Groups: An Introduction to Lie Group Theory
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Matrix Groups: An Introduction to Lie Group Theory |
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Matrix Groups: An Introduction to Lie Group Theory |
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基本信息·出版社：Springer
·页码：343 页
·出版日期：2003年10月
·ISBN：1852334703
·International Standard Book Number：1852334703
·条形码：9781852334703
·EAN：9781852334703
·装帧：平装
·正文语种：英语
内容简介 Throughout the text, the emphasis is on providing an approach that is accessible to 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 developed theory, preparing students for a more standard and abstract course in Lie theory and differential geometry.
媒体推荐 From the reviews of the first edition:
MATHEMATICAL REVIEWS
"This excellent book gives an easy introduction to the theory of Lie groups and Lie algebras by restricting the material to real and complex matrix groups. This provides the reader not only with a wealth of examples, but it also makes the key concepts much more concrete. This combination makes the material in this book more easily accessible for the readers with a limited background…The book is very easy to read and suitable for an elementary course in Lie theory aimed at advanced undergraduates or beginning graduate students…To summarize, this is a well-written book, which is highly suited as an introductory text for beginning graduate students without much background in differential geometry or for advanced undergraduates. It is a welcome addition to the literature in Lie theory."
"This book is an introduction to Lie group theory with focus on the matrix case. … This book can be recommended to students, making Lie group theory more accessible to them." (A. Akutowicz, Zentralblatt MATH, Vol. 1009, 2003)
目录 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.- Bibliography.- Index.
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