Structure and Geometry of Lie Groups
(Sprache: Englisch)
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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Produktinformationen zu „Structure and Geometry of Lie Groups “
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.
Klappentext zu „Structure and Geometry of Lie Groups “
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.
Inhaltsverzeichnis zu „Structure and Geometry of Lie Groups “
Preface.- 1 Introduction.- Part I Matrix Groups.- 2 Concrete Matrix Groups.- 3 The Matrix Exponential Function.- 4 Linear Lie Groups.- Part II Lie Algebras.- 5 Elementary Structure Theory of Lie Algebras.- 6 Root Decomposition.- 7 Representation Theory of Lie Algebras.- Part III Manifolds and Lie Groups.- 8 Smooth Manifolds.- 9 Basic Lie Theory.- 10 Smooth Actions of Lie Groups.- Part IV Structure Theory of Lie Groups.- 11 Normal Subgroups, Nilpotemt and Solvable Lie Groups.- 12 Compact Lie Groups.- 13 Semisimple Lie Groups.- 14 General Structure Theory.- 15 Complex Lie Groups.- 16 Linearity of Lie Groups.- 17 Classical Lie Groups.- 18 Nonconnected Lie Groups.- Part V Appendices.- A Basic Covering Theory.- B Some Multilinear Algebra.- C Some Functional Analysis.- D Hints to Exercises.- References.- Index.
Bibliographische Angaben
- Autoren: Joachim Hilgert , Karl-Hermann Neeb
- 2011, 2012, X, 746 Seiten, Masse: 16 x 24,1 cm, Gebunden, Englisch
- Verlag: Springer, Berlin
- ISBN-10: 0387847936
- ISBN-13: 9780387847931
- Erscheinungsdatum: 05.11.2011
Sprache:
Englisch
Rezension zu „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)
Pressezitat
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)
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