李群论
2013-1
世界图书出版公司
Claude Chevalley
217
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Expository books on the theory of Lie groups generally confine
themselves to the local aspect of the theory.This limitation was
probably necessary as long as general topology was not yet
sufficiently well elaborated to provide a solid base for a theory
in the large.These days are now passed， and we have thought that it
would be'useful to have a systematic treatment of the theory from a
global point of view. The present volume introduces the main basic
principles which govern the theory of Lie groups.
A Lie group is at the same time a group， a topological space and
a manifold: it has therefore three kinds of "structures，" which are
interrelated with each other.The elem，entary properties of
abstractgroups are by now sufficiently well known to the general
mathematical public to make it unnecessary for such a book as this
one to contain a purely group-theoretic chapter.The theory of
topological groups， however， has been included and is treated in
Chapter II. The great- est part of this chapteris concerned with
the theory of covering spaces and groups， which is developed
independently from the theory of paths. Chapter III is concerned
with the theory of （analytic） mani-folds （independently of the
notion of group）.Our definition of a manifold is inspired by the
definition of a Riemann surface given by H. Weyl in his book。‘Die
Idee der Riemannschen Flache"; it has， compared with the definition
by overlapping system of coordinates， the advantage of being
intrinsic.The theory of involutive systems of differential
equations on a manifold is treated not only from the local point of
view but also in the large. In order to achieve this， a defini-tion
of the submanifolds of a manifold is given according to which a
submanifold is not necessarily a topological subspace of the
manifold in which it is imbedded.
作者：（美国）科沃里（Claude Chevalley）
INTRODCTION
Ⅰ.THE CLASSICAL LINEAR GROUPS
Ⅱ.TOPOLIGIVAL GROUPS
Ⅲ.MANIFOLDS
Ⅳ.ANAKYTIC GROUPS.LIE GROUPS
Ⅴ.THE DIFFERENTIAL CALCULUS OF CARTAN
Ⅵ.COMPACT LIE AND THEIR REPRESENTATIONG
INDEX
版权页： 插图：
《李群论(英文版)》由世界图书出版公司北京公司出版。
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由于书写的比较早，里面的记号和现在的很不一样，其中微分流形的定义都和我们平时所见的不太相同。不太适合用来学习，但作为参考辅助是很不错的。很怀疑普林斯顿大学为什么将他们的书出版的很晚，比成书的时间晚了近50年。
比打印版的清楚。正在都Knapp的书，以此作为补充材料。只是INDEX不够全面，这个有点遗憾。而且里面的定义与现在的模样稍有不同。