中文名: 李群
原名: Lie Groups
作者: Daniel Bump
图书分类: 教育/科技
版本: 英文影印版
出版社: 世界图书出版公司
书号: 9787510005008
发行时间: 2009年
地区: 大陆
语言: 英文
简介:
李群 (英文版)(Lie Groups)
基本信息
·出版社：世界图书出版公司
·页码：451 页
·出版日期：2009年08月
·ISBN：9787510005008
·条形码：9787510005008
·包装版本：第1版
·装帧：平装
·开本：24
·正文语种：英语
·外文书名：Lie Groups
扫描分辨率：600 dpi; 467s
内容简介
Part I covers standard general properties of representations of compactgroups （including Lie groups and other compact groups, such as finite or p-adie ones）. These include Schur orthogonality, properties of matrix coefficientsand the Peter-Weyl Theorem.
Part II covers the fundamentals of Lie gronps, by which I mean those sub-jects that I think are most urgent for the student to learn. These include thefollowing topics for compact groups: the fundamental group, the conjngacyof maximal tori （two proofs）, and the Weyl character formula. For noncom-pact groups, we start with complex analytic groups that are obtained bycomplexification of compact Lie groups, obtaining the lwasawa and Bruhatdecompositions. These arc the reductive complex groups. They are of course aspecial case, bnt a good place to start in the noncompact world. More generalnoncompact Lie groups with a Cartan decomposition are studied in the lastfew chapters of Part II. Chapter 31, on symmetric spaces, alternates exampleswith theory, discussing the embedding of a noncompact symmetric space inits compact dnal, the boundary components and Bergman-Shilov boundaryof a symmetric tube domain, anti Cartan's classification. Chapter 32 con-structs the relative root system, explains Satake diagrams and gives examplesillustrating the various phenomena that can occur, and reproves the Iwasawadecomposition, formerly obtained for complex analytic groups, in this moregeneral context. Finally, Chapter 33 surveys the different ways Lie groups canbe embedded in oue another.
