This book provides an introduction to Lie groups, Lie algebras, and representation theory, aimed at graduate students in mathematics and physics.Although there are already several excellent books that cover many of the same topics, this book has two distinctive features that I hope will make it auseful addition to the literature. First, it treats Lie groups (not just Lie alge bras) in a way that minimizes the amount of manifold theory needed. Thus,I neither assume a prior course on differentiable manifolds nor provide a con-densed such course in the beginning chapters. Second, this book provides a gentle introduction to the machinery of semisimple groups and Lie algebras bytreating the representation theory of SU(2) and SU(3) in detail before going to the general case. This allows the reader to see roots, weights, and the Weyl group "in action" in simple cases before confronting the general theory.The standard books on Lie theory begin immediately with the general case:a smooth manifold that is also a group. The Lie algebra is then defined as the space of left-invariant vector fields and the exponential mapping is defined in terms of the flow along such vector fields. This approach is undoubtedly the right one in the long run, but it is rather abstract for a reader encountering such things for the first time. Furthermore, with this approach, one must either assume the reader is familiar with the theory of differentiable manifolds (which rules out a substantial part of one's audience) or one must spend considerable time at the beginning of the book explaining this theory (in which case, it takes a long time to get to Lie theory proper).
this book provides an introduction to lie groups, lie algebras, and representation theory, aimed at graduate students in mathematics and physics.although there are already several excellent books that cover many of the same topics, this book has two distinctive features that i hope will make it auseful addition to the literature. first, it treats lie groups (not just lie alge bras) in a way that minimizes the amount of manifold theory needed. thus,i neither assume a prior course on differentiable manifolds nor provide a con-densed such course in the beginning chapters. second, this book provides a gentle introduction to the machinery of semisimple groups and lie algebras bytreating the representation theory of su(2) and su(3) in detail before going to the general case. this allows the reader to see roots, weights, and the weyl group "in action" in simple cases before confronting the general theory.
the standard books on lie theory begin immediately with the general case:a smooth manifold that is also a group. the lie algebra is then defined as the space of left-invariant vector fields and the exponential mapping is defined in terms of the flow along such vector fields. this approach is undoubtedly the right one in the long run, but it is rather abstract for a reader encountering such things for the first time. furthermore, with this approach, one must either assume the reader is familiar with the theory of differentiable manifolds (which rules out a substantial part of one's audience) or one must spend considerable time at the beginning of the book explaining this theory (in which case, it takes a long time to get to lie theory proper).
This book provides an introduction to Lie groups, Lie algebras, and representation theory, aimed at graduate students in mathematics and physics.Although there are already several excellent books that cover many of the same topics, this book has two distinctive features that I hope will make it auseful addition to the literature. First, it treats Lie groups (not just Lie alge bras) in a way that minimizes the amount of manifold theory needed. Thus,I neither assume a prior course on differentiable manifolds nor provide a con-densed such course in the beginning chapters. Second, this book provides a gentle introduction to the machinery of semisimple groups and Lie algebras bytreating the representation theory of SU(2) and SU(3) in detail before going to the general case. This allows the reader to see roots, weights, and the Weyl group "in action" in simple cases before confronting the general theory.The standard books on Lie theory begin immediately with the general case:a smooth manifold that is also a group. The Lie algebra is then defined as the space of left-invariant vector fields and the exponential mapping is defined in terms of the flow along such vector fields. This approach is undoubtedly the right one in the long run, but it is rather abstract for a reader encountering such things for the first time. Furthermore, with this approach, one must either assume the reader is familiar with the theory of differentiable manifolds (which rules out a substantial part of one's audience) or one must spend considerable time at the beginning of the book explaining this theory (in which case, it takes a long time to get to Lie theory proper).
马上开口说韩语-含附册-赠送MP3光盘 本书特色 《马上开口说韩语》:出国旅游、工作、学习、生活应急**。流利口语,即学即用,超大容量,1000余句口语超实用。...
先秦的文献、文学与文化:高华平自选集 本书特色 iv id="bjtj" style="word-wrap: break-word; word-break: b...
少儿注音彩图版·影响孩子一生的世界十大名著:海底两万里 本书特色 阅览全世界流传*广的文学名著,收藏*值得珍爱的世界经典美文。由国内一流手绘插画师精绘极富艺术与...
实用秘书学 本书特色 本书主要内容为秘书从业人员职能和具体工作操作要求,包括秘书从业标准与礼仪、办公室日常事务管理、常用公文写作、会议流程管理、商务活动管理、商...
汉英笔译全译实践教程 本书特色 全书共设20个主题,涵盖教育、旅游、商品广告、娱乐、文学、婚姻家庭、医药卫生、历史文化、法律 、艺术、资源环保、新闻媒体、国际贸...
儒林外史-中国古典文学名著-无障碍阅读-青少版 本书特色 吴敬梓编著的《儒林外史》是我国文学史上一部杰出的现实主义的长篇讽刺小说。书中所表现的是作者吴敬梓亲身的...
环境工程CAD设计与应用 本书特色 本书**版经两次重印,深受广大读者的喜爱。本次修订选择autocad 2008中文版为蓝本,其操作界 面、提示以及帮助文件等...
帮你走进作文大门:小学生作文入门五十四讲 本书特色 《帮你走进作文大门》共五十讲,内容紧紧围绕小学生作文的“字、词、句、段、篇”和“语(语法)、修(修辞...
幼儿教师音乐知识与技能 本书特色 本丛书是国内**部全面指导农村幼儿教育的大型丛书涵盖农村幼儿教育的理论与实践的主要内容具有时代性、针对性、实用性、通俗性了解农...
★ 重新认识印刷出版的力量********************编辑推荐********************印刷在法国大革命中到底起了什么作用?虽然这个问...
史记-无障碍阅读学生版 本书特色 司马迁的《史记(学生版无障碍阅读)》是我国历 史上**部纪传体通史。它记载了上自黄帝,下至汉 武帝前后三千余年的历史...
高等代数全程导学及习题全解(北京大学第三版) 内容简介 高等代数主要包括多项和线性代数几部分内容,这些都是进一步学习数学各个分支以及其它理、工学科的基础。高等代...
Intwenty-first-centuryChina,socialisteducationaltraditionshavegivenwaytopractice...
钢铁是怎样炼成的-(青少版) 本书特色 《钢铁是怎样炼成的(青少版)》由上海人民美术出版社出版。怎样从一个普通的工人,成长为一个无产阶级英雄的故事,为我们描绘了...
4年级-小学生英语阅读2+1强化训练-名师手把手--赠送MP3光盘 本书特色 《方洲新概念?名师手把手?小学生英语阅读2+1强化训练:4年级》以教师参考用书为标...
宝石狗 本书特色 本书所选的29个童话充满浪漫的想象,多发生在乡村里,通过讲述小熊、小兔子、小老鼠、小松鼠、大黑猫等小动物们发生的温情童话,勾画了儿童内心世界的...
混凝土结构平法识图 本书特色 本书按照*新国家建筑标准图集《混凝土结构施工图平面整体表示方法制图规则和构造详图》 (11g101)及高等院校土建类相关专业的教学...
税务稽查案件查办实务及典型案例 内容简介 本书以税务稽查案件查办为主线, 对现行税务稽查相关法律、行政法规、部门规章、规范性文件等进行了梳理、整合, 参照了部分...
说话接龙系列丛书生字开花(2年级下) 本书特色 丁惠臻老师独创的“主题积累、接龙激活、习作运用”说话接龙教学法享誉国内,参与实验的学生个个思维敏捷、能言善辩。《...
高等数学题解词典:问题与解答 内容简介 本书是一本以题解为中心的比较全面、系统、实用的工具书。内容包括函数、极限、连续、一元函数微分学、不定积分、定积分、空间解...