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Zusatztext 'A nice feature of this book is a variety of problems proposed at the end of each section; this makes it especially suitable as a textbook for a first course in Lie groups, addressed to an audience of mathematicians or physicists. MMA Reviews, March 2007, Fabio Mainardi Klappentext This book is 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 isdeveloped in its local and global aspects. The classical groups are analyzed 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! root! weights and reflections. The fundamental groups of theclassical 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. Zusammenfassung This new in paperback edition provides a clear introduction to the theory of Lie groups and their representations for advanced undergraduates and graduate students in mathematics. Starting from basic undergraduate level mathematics, the text proceeds through the fundamentals of Lie theory up to topics in representation theory. Inhaltsverzeichnis Preface 1: The exponential map 2: Lie theory 3: The classical groups 4: Manifolds, homogeneous spaces, Lie groups 5: Integration 6: Representations Appendix: Analytic Functions and Inverse Function Theorem References Index ...
