Lie groups and Lie algebras

著者

• Bourbaki, Nicolas

書誌事項

Lie groups and Lie algebras

Nicolas Bourbaki

（Elements of mathematics / Nicolas Bourbaki）

Springer-Verlag, c1988-

• Chapters 1-3 : us
• Chapters 1-3 : gw
• Chapters 1-3 : gw : softcover
• Chapters 4-6 : gw
• Chapters 4-6 : gw : softcover
• Chapters 7-9 : gw
• Chapters 7-9 : gw : softcover

タイトル別名

Groupes et algèbres de Lie

注記

Translation of: Groupes et algèbres de Lie. (Éléments de mathématique)

Translator: Andrew Pressley. Cf. t.p. verso

Bibliography: v. chapters 1-3, p. 430-433; v. chapters 4-6, p. [255]-257

Includes index

内容説明・目次

巻冊次

Chapters 4-6 : gw ISBN 9783540426509

内容説明

From the reviews of the French edition: "This is a rich and useful volume. The material it treats has relevance well beyond the theory of Lie groups and algebras, ranging from the geometry of regular polytopes and paving problems to current work on finite simple groups having a (B,N)-pair structure, or 'Tits systems'". --G.B. Seligman in MathReviews.

目次

Coxeter Groups and Tits Systems.- Groups Generated by Reflections.- Root Systems.

巻冊次

Chapters 7-9 : gw ISBN 9783540434054

内容説明

This is the softcover reprint of the English translation of Bourbaki's text Groupes et Algebres de Lie, Chapters 7 to 9. It completes the previously published translations of Chapters 1 to 3 (3-540-64242-0) and 4 to 6 (978-3-540-69171-6) by covering the structure and representation theory of semi-simple Lie algebras and compact Lie groups. Chapter 7 deals with Cartan subalgebras of Lie algebras, regular elements and conjugacy theorems. Chapter 8 begins with the structure of split semi-simple Lie algebras and their root systems. It goes on to describe the finite-dimensional modules for such algebras, including the character formula of Hermann Weyl. It concludes with the theory of Chevalley orders. Chapter 9 is devoted to the theory of compact Lie groups, beginning with a discussion of their maximal tori, root systems and Weyl groups. It goes on to describe the representation theory of compact Lie groups, including the application of integration to establish Weyl's formula in this context. The chapter concludes with a discussion of the actions of compact Lie groups on manifolds. The nine chapters together form the most comprehensive text available on the theory of Lie groups and Lie algebras.

目次

Cartan Subalgebras and Regular Elements.- Split Semi-simple Lie Algebras.- Compact Real Lie Groups.

巻冊次

Chapters 1-3 : gw ISBN 9783540502180

内容説明

This is the softcover reprint of the 1975 English translation of the first three chapters of Bourbaki's Groupes et algebres de Lie. The first chapter describes the theory of Lie algebras, their deviations, representations, and enveloping algebras. Chapter two introduces free Lie algebras in order to discuss the exponential, logarithmic and the Hausdorff series. Chapter three deals with the theory of Lie groups over R and C ultrametric fields.

目次

• Lie Algebras
• Free Lie Algebras
• Lie Groups, Historical Notes
• Exercises,

巻冊次

Chapters 1-3 : gw : softcover ISBN 9783540642428

内容説明

This is the softcover reprint of the 1975 English translation of the first three chapters of Bourbaki's Groupes et algebres de Lie. The first chapter describes the theory of Lie algebras, their deviations, representations, and enveloping algebras. Chapter two introduces free Lie algebras in order to discuss the exponential, logarithmic and the Hausdorff series. Chapter three deals with the theory of Lie groups over R and C ultrametric fields.

目次

• Lie Algebras
• Free Lie Algebras
• Lie Groups, Historical Notes
• Exercises,

巻冊次

Chapters 7-9 : gw : softcover ISBN 9783540688518

内容説明

This is the softcover reprint of the English translation of Bourbaki's text Groupes et Algebres de Lie, Chapters 7 to 9. It completes the previously published translations of Chapters 1 to 3 (3-540-64242-0) and 4 to 6 (978-3-540-69171-6) by covering the structure and representation theory of semi-simple Lie algebras and compact Lie groups. Chapter 7 deals with Cartan subalgebras of Lie algebras, regular elements and conjugacy theorems. Chapter 8 begins with the structure of split semi-simple Lie algebras and their root systems. It goes on to describe the finite-dimensional modules for such algebras, including the character formula of Hermann Weyl. It concludes with the theory of Chevalley orders. Chapter 9 is devoted to the theory of compact Lie groups, beginning with a discussion of their maximal tori, root systems and Weyl groups. It goes on to describe the representation theory of compact Lie groups, including the application of integration to establish Weyl's formula in this context. The chapter concludes with a discussion of the actions of compact Lie groups on manifolds. The nine chapters together form the most comprehensive text available on the theory of Lie groups and Lie algebras.

目次

Cartan Subalgebras and Regular Elements.- Split Semi-simple Lie Algebras.- Compact Real Lie Groups.

巻冊次

Chapters 4-6 : gw : softcover ISBN 9783540691716

内容説明

From the reviews of the French edition: "This is a rich and useful volume. The material it treats has relevance well beyond the theory of Lie groups and algebras, ranging from the geometry of regular polytopes and paving problems to current work on finite simple groups having a (B,N)-pair structure, or 'Tits systems'". --G.B. Seligman in MathReviews.

目次

Coxeter Groups and Tits Systems.- Groups Generated by Reflections.- Root Systems.

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詳細情報

• NII書誌ID(NCID): BA05026741
• ISBN:
  • 0387502181
  • 3540502181
  • 3540642420
  • 3540426507
  • 9783540691716
  • 3540434054
  • 9783540688518
• LCCN: 88031203
• 出版国コード: gw
• タイトル言語コード: eng
• 本文言語コード: eng
• 原本言語コード: fre
• 出版地: Berlin ; Tokyo
• ページ数/冊数: 4 v.
• 大きさ: 24 cm
• 分類:
  • LCC : QA387
  • DC19 : 512/.55
  • NDC7 : 410
  • NDC7 : 411.65
• 件名:
  • LCSH : Lie groups
  • LCSH : Lie algebras
• 親書誌ID:
  • BA01043035