Structure and Geometry of Lie Groups

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This book introduces Lie groups and their actions on manifolds and provides in-depth applications of fundamental principles, while remaining accessible to a range of mathematicians and graduate students. Includes appendices on theory and multilinear algebra.
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This textbook is ideal for advanced undergraduate or first-graduate students who want to learn the fundamentals of Lie groups. It covers the principles behind the theory and includes numerous applications and examples. The author's approach is unique - where some texts develop Lie group theory from matrix groups, differential geometry plays a more prominent role in this book. Most students will not have a background in differential geometry and for that reason, the authors have included an introduction to the topic that begins at the ground level. Each section engages the reader in an in-depth instruction on some of the most important, yet basic principles of Lie theory. In addition to these core topics, the authors include more recent research.
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Matrix Groups.- Concrete Matrix Groups. The Matrix Exponential Function. Linear Lie Groups. Lie Algebras.- Elementary Structure Theory of Lie Algebras. Root Decomposition. Representation Theory of Lie Algebras.
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This self-contained text is an excellent introduction to Lie groups and their actions on manifolds. The authors start with an elementary discussion of matrix groups, followed by chapters devoted to the basic structure and representation theory of finite dimensinal Lie algebras. They then turn to global issues, demonstrating the key issue of the interplay between differential geometry and Lie theory. Special emphasis is placed on homogeneous spaces and invariant geometric structures. The last section of the book is dedicated to the structure theory of Lie groups. Particularly, they focus on maximal compact subgroups, dense subgroups, complex structures, and linearity.This text is accessible to a broad range of mathematicians and graduate students; it will be useful both as a graduate textbook and as a research reference.
Autor: Joachim Hilgert, Karl-Hermann Neeb
Joachim Hilgert forscht und lehrt am Institut für Mathematik der Universität Paderborn.

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Autor: Joachim Hilgert
ISBN-13 :: 9780387847931
ISBN: 0387847936
Erscheinungsjahr: 05.11.2011
Verlag: Springer-Verlag GmbH
Gewicht: 1242g
Seiten: 744
Sprache: Englisch
Sonstiges: Buch, 244x167x48 mm, 4 schwarz-weiße Abbildungen
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