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Structure and Geometry of Lie Groups
Taschenbuch von Karl-Hermann Neeb (u. a.)
Sprache: Englisch

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Beschreibung
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.
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.
Zusammenfassung

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.

Students gain the ability to work through problems following the basic principles of Lie theory, understand references to Lie theoretic concepts, and easily move on to more advanced topics.

Inhaltsverzeichnis
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.
Details
Erscheinungsjahr: 2014
Fachbereich: Arithmetik & Algebra
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Seiten: 756
Reihe: Springer Monographs in Mathematics
Inhalt: x
746 S.
4 s/w Illustr.
ISBN-13: 9781489990068
ISBN-10: 1489990062
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Neeb, Karl-Hermann
Hilgert, Joachim
Auflage: 2012
Hersteller: Springer New York
Springer US, New York, N.Y.
Springer Monographs in Mathematics
Maße: 235 x 155 x 41 mm
Von/Mit: Karl-Hermann Neeb (u. a.)
Erscheinungsdatum: 25.01.2014
Gewicht: 1,124 kg
preigu-id: 105468414
Zusammenfassung

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.

Students gain the ability to work through problems following the basic principles of Lie theory, understand references to Lie theoretic concepts, and easily move on to more advanced topics.

Inhaltsverzeichnis
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.
Details
Erscheinungsjahr: 2014
Fachbereich: Arithmetik & Algebra
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Seiten: 756
Reihe: Springer Monographs in Mathematics
Inhalt: x
746 S.
4 s/w Illustr.
ISBN-13: 9781489990068
ISBN-10: 1489990062
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Neeb, Karl-Hermann
Hilgert, Joachim
Auflage: 2012
Hersteller: Springer New York
Springer US, New York, N.Y.
Springer Monographs in Mathematics
Maße: 235 x 155 x 41 mm
Von/Mit: Karl-Hermann Neeb (u. a.)
Erscheinungsdatum: 25.01.2014
Gewicht: 1,124 kg
preigu-id: 105468414
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