Science/Engineering Lie Groups: An Introduction through Linear Groups (0198596839)

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Lie Groups: An Introduction through Linear Groups

This book is intended as an introduction to the theory of Lie groups and their representations at the advanced undergraduate or beginning graduate level. It covers the essentials of the subject starting from basic undergraduate mathematics. The correspondence between linear Lie groups and Lie algebras is developed in its local and global aspects. The classical groups are analysed in detail, first with elementary matrix methods, then with the help of the structural tools typical of the theory of semisimple groups, such as Cartan subgroups, roots, weights, and reflections. The fundamental groups of the classical groups are worked out as an application of these methods. Manifolds are introduced when needed, in connection with homogeneous spaces, and the elements of differential and integral calculus on manifolds are presented, with special emphasis on integration on groups and homogeneous spaces. Representation theory starts from first principles, such as Schur's lemma and its consequences, and proceeds from there to the Peter- Weyl theorem, Weyl's character formula, and the Borel-Weil theorem, all in the context of linear groups.

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	Representation of Linear Groups An Introduction Based on Examples from Physics and Number Theory Rolf Berndt, " Representation of Linear Groups An Introduction Based on Examples from Physics and Number Theory" Friedr Vieweg & Sohn Verlagsgesellschaft (January 2007) \| ISBN: 3834803197 \| 270 pages \| PDF \| 1,6 Mb ...
	Science/Engineering Groups, Graphs and Trees: An Introduction to the Geometry of Infinite Groups Groups, Graphs and Trees: An Introduction to the Geometry of Infinite GroupsPublisher: Cambridge University Press \| Pages: 256 \| 2008-09-01 \| ISBN: 0521895456\| PDF \| 2 MBProduct Description:This outstanding new book presents the modern, geo ...
	Encyclopedias Algebra IV: Infinite Groups, Linear Groups (Encyclopaedia of Mathematical Sciences) Algebra IV: Infinite Groups, Linear Groups (Encyclopaedia of Mathematical Sciences)Springer \| 1993 \| ISBN: 0387533729 \| Pages: 103 \| DJVU \| 8.18 MBGroup theory is one of the most fundamental branches of mathematics. This volume of the Encyc ...
	Science/Engineering Groups and Symmetries: From Finite Groups to Lie Groups Yvette Kosmann-Schwarzbach, "Groups and Symmetries: From Finite Groups to Lie Groups" Springer \| 2009 \| ISBN: 0387788654 \| 194 pages \| PDF \| 2,2 MB The theory of group representations is a fundamental subject at the intersection of alge ...
	Study Groups as Galois Groups: An Introduction (Cambridge Studies in Advanced Mathematics) Helmut Volklein "Groups as Galois Groups: An Introduction (Cambridge Studies in Advanced Mathematics)"Cambridge University Press \| English \| 1996 \| ISBN: 0521065038 \| 266 pages \| DJVU \| 1,2 MBThis book describes various approaches to the In ...
	Introduction to Complex Reflection Groups and Their Braid Groups (Lecture Notes in Mathematics) Michel Broué "Introduction to Complex Reflection Groups and Their Braid Groups (Lecture Notes in Mathematics)"Springer \| English \| 2010-03-01 \| ISBN: 3642111742 \| 132 pages \| PDF \| 1 MBWeyl groups are particular cases of complex reflectio ...

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