Lie groups : an introduction through linear groups

Wulf Rossmann

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

「Nielsen BookData」より

[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

この本の情報

書名 Lie groups : an introduction through linear groups
著作者等 Rossmann, Wulf
シリーズ名 Oxford graduate texts in mathematics
出版元 Oxford University Press
刊行年月 2002
ページ数 x, 265 p.
大きさ 24 cm
ISBN 0198596839
NCID BA55583014
※クリックでCiNii Booksを表示
言語 英語
出版国 イギリス
この本を: 
このエントリーをはてなブックマークに追加

このページを印刷

外部サイトで検索

この本と繋がる本を検索

ウィキペディアから連想