Lie Groups : Beyond an Introduction

Anthony W. Knapp

ISBN 10: 0817642595 / ISBN 13: 9780817642594

Editore: Birkhäuser Boston, Birkhäuser Boston, 2002

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Druck auf Anfrage Neuware - Printed after ordering - Lie Groups Beyond an Introduction takes the reader from the end of introductory Lie group theory to the threshold of infinite-dimensional group representations. Merging algebra and analysis throughout, the author uses Lie-theoretic methods to develop a beautiful theory having wide applications in mathematics and physics. A feature of the presentation is that it encourages the reader's comprehension of Lie group theory to evolve from beginner to expert: initial insights make use of actual matrices, while later insights come from such structural features as properties of root systems, or relationships among subgroups, or patterns among different subgroups.Topics include a description of all simply connected Lie groups in terms of semisimple Lie groups and semidirect products, the Cartan theory of complex semisimple Lie algebras, the Cartan-Weyl theory of the structure and representations of compact Lie groups and representations of complex semisimple Lie algebras, the classification of real semisimple Lie algebras, the structure theory of noncompact reductive Lie groups as it is now used in research, and integration on reductive groups. Many problems, tables, and bibliographical notes complete this comprehensive work, making the text suitable either for self-study or for courses in the second year of graduate study and beyond.

Codice articolo 9780817642594

Dati bibliografici

• Titolo: Lie Groups : Beyond an Introduction
• Editore: Birkhäuser Boston, Birkhäuser Boston
• Data di pubblicazione: 2002
• Lingua: Inglese
• ISBN 10: 0817642595
• ISBN 13: 9780817642594
• Rilegatura: Buch
• Edizione: seconda edizione
• Condizione: Neu
• Dimensioni: 241 L x 160 A x 49 P (millimetri) 241 millimetri di larghezza per 160 millimetri di altezza per 49 millimetri di profondità
• Peso: 1402 grammi

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Riassunto

<p>This book takes the reader from the end of introductory Lie group theory to the threshold of infinite-dimensional group representations. Merging algebra and analysis throughout, the author uses Lie-theoretic methods to develop a beautiful theory having wide applications in mathematics and physics. The book initially shares insights that make use of actual matrices; it later relies on such structural features as properties of root systems.</p>

Dalla quarta di copertina

<p><em>Lie Groups Beyond an Introduction</em> takes the reader from the end of introductory Lie group theory to the threshold of infinite-dimensional group representations. Merging algebra and analysis throughout, the author uses Lie-theoretic methods to develop a beautiful theory having wide applications in mathematics and physics. A feature of the presentation is that it encourages the reader's comprehension of Lie group theory to evolve from beginner to expert: initial insights make use of actual matrices, while later insights come from such structural features as properties of root systems, or relationships among subgroups, or patterns among different subgroups.</p><p>Topics include a description of all simply connected Lie groups in terms of semisimple Lie groups and semidirect products, the Cartan theory of complex semisimple Lie algebras, the Cartan-Weyl theory of the structure and representations of compact Lie groups and representations of complex semisimple Lie algebras, the classification of real semisimple Lie algebras, the structure theory of noncompact reductive Lie groups as it is now used in research, and integration on reductive groups. Many problems, tables, and bibliographical notes complete this comprehensive work, making the text suitable either for self-study or for courses in the second year of graduate study and beyond. </p>