Structure and Geometry of Lie Groups

Joachim Hilgert, Karl-Hermann Neeb

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English

Springer-Verlag New York Inc.
25 January 2014

Algebra; Groups & group theory; Differential & Riemannian geometry; Algebraic topology

Series: Springer Monographs in Mathematics

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.

By: Joachim Hilgert, Karl-Hermann Neeb
Imprint: Springer-Verlag New York Inc.
Country of Publication: United States
Edition: 2012 ed.
Dimensions: Height: 235mm, Width: 155mm, Spine: 38mm
Weight: 1.139kg
ISBN: 9781489990068
ISBN 10: 1489990062
Series: Springer Monographs in Mathematics
Pages: 746
Publication Date: 25 January 2014
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

Reviews for Structure and Geometry of Lie Groups

From the reviews: The monograph under review is an introduction to the structure theory and geometry of Lie groups accessible both to a broad range of mathematicians and to graduate students. ... The book consists of twenty one chapters divided into five parts. It starts with an introduction which presents the structure of the book, contains various teaching suggestions and introduces some fundamental notation. (Volodymyr Mazorchuk, Zentralblatt MATH, Vol. 1229, 2012)