Normal view MARC view ISBD view

Lie groups beyond an introduction / Anthony W. Knapp.

By: Knapp, Anthony W.
Material type: materialTypeLabelBookSeries: Progress in mathematics (Boston, Mass.): v. 140.Publisher: Boston : Birkhäuser, c2002Edition: 2nd ed.Description: xviii, 812 p. : il. ; 24 cm.ISBN: 0817642595 (acidfree paper); 3764342595 (Basel : acid-free paper).Subject(s): Lie groups | Lie algebras | Representations of Lie groupsOther classification: 22-01
Contents:
Preface to the Second Edition xi -- Preface to the First Edition xiii -- List of Figures xvi -- Prerequisites by Chapter xvii -- Standard Notation xviii -- INTRODUCTION: CLOSED LINEAR GROUPS [1] -- 1. Linear Lie Algebra of a Closed Linear Group [1] -- 2. Exponential of a Matrix [6] -- 3. Closed Linear Groups [9] -- 4. Closed Linear Groups as Lie Groups [11] -- 5. Homomorphisms [16] -- 6. Problems [20] -- I. LIE ALGEBRAS AND LIE GROUPS [23] -- 1. Definitions and Examples [24] -- 2. Ideals [29] -- 3. Field Extensions and the Killing Form [33] -- 4. Semidirect Products of Lie Algebras [38] -- 5. Solvable Lie Algebras and Lie’s Theorem [40] -- 6. Nilpotent Lie Algebras and Engel’s Theorem [45] -- 7. Cartan’s Criterion for Semisimplicity [49] -- 8. Examples of Semisimple Lie Algebras [56] -- 9. Representations of sl(2, C) [62] -- 10. Elementary Theory of Lie Groups [68] -- 11. Covering Groups [81] -- 12. Complex Structures [91] -- 13. Aside on Real-analytic Structures [98] -- 14. Automorphisms and Derivations [100] -- 15. Semidirect Products of Lie Groups [102] -- 16. Nilpotent Lie Groups [106] -- 17. Classical Semisimple Lie Groups [110] -- 18. Problems [118] -- II. COMPLEX SEMISIMPLE LIE ALGEBRAS [123] -- 1. Classical Root-space Decompositions [124] -- 2. Existence of Cartan Subalgebras [129] -- 3. Uniqueness of Cartan Subalgebras [137] -- 4. Roots [140] -- 5. Abstract Root Systems [149] -- 6. Weyl Group [162] -- 7. Classification of Abstract Cartan Matrices [170] -- 8. Classification of Nonreduced Abstract Root Systems [184] -- 9. Serre Relations [186] -- 10. Isomorphism Theorem [196] -- 11. Existence Theorem [199] -- 12. Problems [203] -- III. UNIVERSAL ENVELOPING ALGEBRA [213] -- 1. Universal Mapping Property [213] -- 2. Poincar6-Birkhoff-Witt Theorem [217] -- 3. Associated Graded Algebra [222] -- 4. Free Lie Algebras [228] -- 5. Problems [229] -- IV. COMPACT LIE GROUPS [233] -- 1. Examples of Representations [233] -- 2. Abstract Representation Theory [238] -- 3. Peter-Weyl Theorem [243] -- 4. Compact Lie Algebras [248] -- 5. Centralizers of Tori [251] -- 6. Analytic Weyl Group [260] -- 7. Integral Forms [264] -- 8. Weyl’s Theorem [268] -- 9. Problems [269] -- V. FINITE-DIMENSIONAL REPRESENTATIONS [273] -- 1. Weights [274] -- 2. Theorem of the Highest Weight [279] -- 3. Verma Modules [283] -- 4. Complete Reducibility [290] -- 5. Harish-Chandra Isomorphism [300] -- V. FINITE-DIMENSIONAL REPRESENTATIONS -- Weyl Character Formula [314] -- Parabolic Subalgebras [325] -- Application to Compact Lie Groups [333] -- Problems [339] -- VI. STRUCTURE THEORY OF SEMISIMPLE GROUPS [347] -- 1. Existence of a Compact Real Form [348] -- 2. Cartan Decomposition on the Lie Algebra Level [354] -- 3. Cartan Decomposition on the Lie Group Level [361] -- 4. Iwasawa Decomposition [368] -- 5. Uniqueness Properties of the Iwasawa Decomposition [378] -- 6. Cartan Subalgebras [384] -- 7. Cayley Transforms [389] -- 8. Vogan Diagrams [397] -- 9. Complexification of a Simple Real Lie Algebra [406] -- 10. Classification of Simple Real Lie Algebras [408] -- 11. Restricted Roots in the Classification [422] -- 12. Problems [426] -- VII. ADVANCED STRUCTURE THEORY [433] -- 1. Further Properties of Compact Real Forms [434] -- 2. Reductive Lie Groups [446] -- 3. KAK Decomposition [458] -- 4. Bruhat Decomposition [460] -- 5. Structure of M [464] -- 6. Real-rank-one Subgroups [470] -- 7. Parabolic Subgroups [474] -- 8. Cartan Subgroups [487] -- 9. Harish-Chandra Decomposition [499] -- 10. Problems [514] -- VIII. INTEGRATION [523] -- 1. Differential Forms and Measure Zero [523] -- 2. Haar Measure for Lie Groups [530] -- 3. Decompositions of Haar Measure [535] -- 4. Application to Reductive Lie Groups [539] -- 5. Weyl Integration Formula [547] -- 6. Problems [552] -- IX. INDUCED REPRESENTATIONS AND BRANCHING THEOREMS [555] -- 1. Infinite-dimensional Representations of Compact Groups [556] -- 2. Induced Representations and Frobenius Reciprocity [563] -- 3. Classical Branching Theorems [568] -- 4. Overview of Branching [571] -- 5. Proofs of Classical Branching Theorems [577] -- 6. Tensor Products and Littlewood-Richardson Coefficients [596] -- 7. Littlewood’s Theorems and an Application [602] -- 8. Problems [609] -- X. PREHOMOGENEOUS VECTOR SPACES [615] -- 1. Definitions and Examples [616] -- 2. Jacobson-Morozov Theorem [620] -- 3. Vinberg’s Theorem [626] -- 4. Analysis of Symmetric Tensors [632] -- 5. Problems [638] -- APPENDICES -- A. Tensors, Filiations, and Gradings -- 1. Tensor Algebra [639] -- 2. Symmetric Algebra [645] -- 3. Exterior Algebra [651] -- 4. Filiations and Gradings [654] -- 5. Left Noetherian Rings [656] -- B. Lie’s Third Theorem -- 1. Levi Decomposition [659] -- 2. Lie’s Third Theorem [662] -- 3. Ado’s Theorem [662] -- 4. Campbell-Baker-Hausdorff Formula [669] -- C. Data for Simple Lie Algebras -- 1. Classical Irreducible Reduced Root Systems [683] -- 2. Exceptional Irreducible Reduced Root Systems [686] -- 3. Classical Noncompact Simple Real Lie Algebras [693] -- 4. Exceptional Noncompact Simple Real Lie Algebras [706] -- Hints for Solutions of Problems [719] -- Historical Notes [751] -- References [783] -- Index of Notation [799] -- Index [805] --
List(s) this item appears in: ÚLTIMOS LIBROS INCORPORADOS
Tags from this library: No tags from this library for this title. Log in to add tags.
    average rating: 0.0 (0 votes)
Item type Home library Shelving location Call number Status Date due Barcode
Libros Libros Instituto de Matemática, CONICET-UNS
Últimas adquisiciones 22 K67-2 (Browse shelf) Available A-9289

Incluye referencias bibliográficas (p. 783-798) e índices.

Preface to the Second Edition xi --
Preface to the First Edition xiii --
List of Figures xvi --
Prerequisites by Chapter xvii --
Standard Notation xviii --
INTRODUCTION: CLOSED LINEAR GROUPS [1] --
1. Linear Lie Algebra of a Closed Linear Group [1] --
2. Exponential of a Matrix [6] --
3. Closed Linear Groups [9] --
4. Closed Linear Groups as Lie Groups [11] --
5. Homomorphisms [16] --
6. Problems [20] --
I. LIE ALGEBRAS AND LIE GROUPS [23] --
1. Definitions and Examples [24] --
2. Ideals [29] --
3. Field Extensions and the Killing Form [33] --
4. Semidirect Products of Lie Algebras [38] --
5. Solvable Lie Algebras and Lie’s Theorem [40] --
6. Nilpotent Lie Algebras and Engel’s Theorem [45] --
7. Cartan’s Criterion for Semisimplicity [49] --
8. Examples of Semisimple Lie Algebras [56] --
9. Representations of sl(2, C) [62] --
10. Elementary Theory of Lie Groups [68] --
11. Covering Groups [81] --
12. Complex Structures [91] --
13. Aside on Real-analytic Structures [98] --
14. Automorphisms and Derivations [100] --
15. Semidirect Products of Lie Groups [102] --
16. Nilpotent Lie Groups [106] --
17. Classical Semisimple Lie Groups [110] --
18. Problems [118] --
II. COMPLEX SEMISIMPLE LIE ALGEBRAS [123] --
1. Classical Root-space Decompositions [124] --
2. Existence of Cartan Subalgebras [129] --
3. Uniqueness of Cartan Subalgebras [137] --
4. Roots [140] --
5. Abstract Root Systems [149] --
6. Weyl Group [162] --
7. Classification of Abstract Cartan Matrices [170] --
8. Classification of Nonreduced Abstract Root Systems [184] --
9. Serre Relations [186] --
10. Isomorphism Theorem [196] --
11. Existence Theorem [199] --
12. Problems [203] --
III. UNIVERSAL ENVELOPING ALGEBRA [213] --
1. Universal Mapping Property [213] --
2. Poincar6-Birkhoff-Witt Theorem [217] --
3. Associated Graded Algebra [222] --
4. Free Lie Algebras [228] --
5. Problems [229] --
IV. COMPACT LIE GROUPS [233] --
1. Examples of Representations [233] --
2. Abstract Representation Theory [238] --
3. Peter-Weyl Theorem [243] --
4. Compact Lie Algebras [248] --
5. Centralizers of Tori [251] --
6. Analytic Weyl Group [260] --
7. Integral Forms [264] --
8. Weyl’s Theorem [268] --
9. Problems [269] --
V. FINITE-DIMENSIONAL REPRESENTATIONS [273] --
1. Weights [274] --
2. Theorem of the Highest Weight [279] --
3. Verma Modules [283] --
4. Complete Reducibility [290] --
5. Harish-Chandra Isomorphism [300] --
V. FINITE-DIMENSIONAL REPRESENTATIONS --
Weyl Character Formula [314] --
Parabolic Subalgebras [325] --
Application to Compact Lie Groups [333] --
Problems [339] --
VI. STRUCTURE THEORY OF SEMISIMPLE GROUPS [347] --
1. Existence of a Compact Real Form [348] --
2. Cartan Decomposition on the Lie Algebra Level [354] --
3. Cartan Decomposition on the Lie Group Level [361] --
4. Iwasawa Decomposition [368] --
5. Uniqueness Properties of the Iwasawa Decomposition [378] --
6. Cartan Subalgebras [384] --
7. Cayley Transforms [389] --
8. Vogan Diagrams [397] --
9. Complexification of a Simple Real Lie Algebra [406] --
10. Classification of Simple Real Lie Algebras [408] --
11. Restricted Roots in the Classification [422] --
12. Problems [426] --
VII. ADVANCED STRUCTURE THEORY [433] --
1. Further Properties of Compact Real Forms [434] --
2. Reductive Lie Groups [446] --
3. KAK Decomposition [458] --
4. Bruhat Decomposition [460] --
5. Structure of M [464] --
6. Real-rank-one Subgroups [470] --
7. Parabolic Subgroups [474] --
8. Cartan Subgroups [487] --
9. Harish-Chandra Decomposition [499] --
10. Problems [514] --
VIII. INTEGRATION [523] --
1. Differential Forms and Measure Zero [523] --
2. Haar Measure for Lie Groups [530] --
3. Decompositions of Haar Measure [535] --
4. Application to Reductive Lie Groups [539] --
5. Weyl Integration Formula [547] --
6. Problems [552] --
IX. INDUCED REPRESENTATIONS AND BRANCHING THEOREMS [555] --
1. Infinite-dimensional Representations of Compact Groups [556] --
2. Induced Representations and Frobenius Reciprocity [563] --
3. Classical Branching Theorems [568] --
4. Overview of Branching [571] --
5. Proofs of Classical Branching Theorems [577] --
6. Tensor Products and Littlewood-Richardson Coefficients [596] --
7. Littlewood’s Theorems and an Application [602] --
8. Problems [609] --
X. PREHOMOGENEOUS VECTOR SPACES [615] --
1. Definitions and Examples [616] --
2. Jacobson-Morozov Theorem [620] --
3. Vinberg’s Theorem [626] --
4. Analysis of Symmetric Tensors [632] --
5. Problems [638] --
APPENDICES --
A. Tensors, Filiations, and Gradings --
1. Tensor Algebra [639] --
2. Symmetric Algebra [645] --
3. Exterior Algebra [651] --
4. Filiations and Gradings [654] --
5. Left Noetherian Rings [656] --
B. Lie’s Third Theorem --
1. Levi Decomposition [659] --
2. Lie’s Third Theorem [662] --
3. Ado’s Theorem [662] --
4. Campbell-Baker-Hausdorff Formula [669] --
C. Data for Simple Lie Algebras --
1. Classical Irreducible Reduced Root Systems [683] --
2. Exceptional Irreducible Reduced Root Systems [686] --
3. Classical Noncompact Simple Real Lie Algebras [693] --
4. Exceptional Noncompact Simple Real Lie Algebras [706] --
Hints for Solutions of Problems [719] --
Historical Notes [751] --
References [783] --
Index of Notation [799] --
Index [805] --

MR, MR1920389

There are no comments for this item.

Log in to your account to post a comment.

Click on an image to view it in the image viewer

¿Necesita ayuda?

Si necesita ayuda para encontrar información, puede visitar personalmente la biblioteca en Av. Alem 1253 Bahía Blanca, llamarnos por teléfono al 291 459 5116, o enviarnos un mensaje a bibima@criba.edu.ar.
Para solicitar copias de artículos, complete el formulario o escríbanos a pedidos.inmabb@gmail.com

Powered by Koha