Lie groups : an introduction through linear groups

著者

• Rossmann, Wulf

書誌事項

Lie groups : an introduction through linear groups

Wulf Rossmann

（Oxford graduate texts in mathematics, 5）

Oxford University Press, 2002

注記

Bibliography: p. 258-260

Includes index

内容説明・目次

内容説明

This book is intended as an introduction to the theory of Lie groups and their representations at the advanced undergraduate or beginning graduate level. It covers the essentials of the subject starting from basic undergraduate mathematics. The correspondence between linear Lie groups and Lie algebras is developed in its local and global aspects. The classical groups are analysed in detail, first with elementary matrix methods, then with the help of the structural tools typical of the theory of semisimple groups, such as Cartan subgroups, roots, weights, and reflections. The fundamental groups of the classical groups are worked out as an application of these methods. Manifolds are introduced when needed, in connection with homogeneous spaces, and the elements of differential and integral calculus on manifolds are presented, with special emphasis on integration on groups and homogeneous spaces. Representation theory starts from first principles, such as Schur's lemma and its consequences, and proceeds from there to the Peter- Weyl theorem, Weyl's character formula, and the Borel-Weil theorem, all in the context of linear groups.

目次

• Preface
• 1. The exponential map
• 2. Lie theory
• 3. The classical groups
• 4. Manifolds, homogeneous spaces, Lie groups
• 5. Integration
• 6. Representations
• Appendix: Analytic Functions and Inverse Function Theorem
• References
• Index

「Nielsen BookData」 より

詳細情報

• NII書誌ID(NCID): BA55583014
• ISBN:
  • 0198596839
• 出版国コード: uk
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: Oxford
• ページ数/冊数: x, 265 p.
• 大きさ: 24 cm
• 親書誌ID:
  • BA31148509