李群論

內(nèi)容概要

　　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?！瓺ie
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.

作者簡介

作者：（美國）科沃里（Claude Chevalley）

書籍目錄

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

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