李群論（英文版） [Theory of Lie Groups] epub pdf mobi txt 電子書下載 2024

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發表於2024-11-25

商品介绍

齣版社：世界圖書齣版公司

ISBN：9787510050657

版次：1

商品編碼：11142975

包裝：平裝

外文名稱：Theory of Lie Groups

開本：24開

齣版時間：2013-01-01

用紙：膠版紙

頁數：213

正文語種：英文

李群論（英文版） [Theory of Lie Groups] epub pdf mobi txt 電子書下載 2024

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內容簡介

　　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.