Lie Groups Beyond an Introduction (Progress in Mathematics) （2ND）

Knapp, Anthony W.

Birkhauser, Boston（2002/09発売）

• 製本 Hardcover:ハードカバー版／ページ数 812 p.
• 言語 ENG
• 商品コード 9780817642594
• DDC分類 512.55

Full Description

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.

Contents

Preface to the Second Edition; Preface to the First Edition; List of Figures; Prerequisites by Chapter; Standard Notation; Introduction: Closed Linear Groups; Lie Algebras and Lie Groups; Complex Semisimple Lie Algebras; Universal Enveloping Algebra; Compact Lie Groups; Finite-Dimensional Representations; Structure Theory of Semisimple Groups; Advanced Structure Theory Integration; Induced Representations and Branching Theorems; Prehomogeneous Vector Spaces; Appendices; Hints for Solutions of Problems; Historical Notes; References; Index of Notation; Index