Holdings: Lectures on Kac-Moody algebras

Lectures on Kac-Moody algebras: proceedings seminar 1986 - 1987

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Bibliographic Details
Main Authors:	Bergvelt, Maarten J. (Author), Kroode, A. P. ten (Author)
Format:	Book
Language:	English
Published:	Amsterdam Centrum voor Wiskunde en Informatica 1992
Series:	Centrum voor Wiskunde en Informatica <Amsterdam>: CWI syllabus 30
Subjects:	Kac-Moody-Algebra Konferenzschrift
Online Access:	Inhaltsverzeichnis
Physical Description:	97 S.

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MARC


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adam_text	CWI SYLLABUS 30 PROCEEDINGS SEMINAR 1986-1987 LECTURES ON KAC-MOODY ALGEBRAS M.J. BERGVELT, A.P.E. TEN KROODE AM CENTRUM VOOR WISKUNDE EN INFONNATICA CENTRE FOR MATHEMATICS AND COMPUTER SCIENCE TABLE OF CONTENTS INTRODUCTION CHAPTER 1 SIMPLE LIE ALGEBRAS 1.0 INTRODUCTION 1 1.1 SIMPLE LIE ALGEBRAS, DEFINITIONS * 1 1.2 SIMPLE LIE ALGEBRAS, EXAMPLES 2 1.3 THE KILLING FORM 3 1.4 CARTAN SUBALGEBRAS 4 1.5 ROOTS AND ROOT SPACES 5 1.6 ROOTS AND ROOT SPACES FOR A/ 6 1.7 FURTHER PROPERTIES OF ROOTS AND ROOT SPACES 7 1.8 SIMPLE ROOTS 9 1.9 GENERATORS AND RELATIONS 10 CHAPTER 2 AFFINE LIE ALGEBRAS [KAC] 2.0 INTRODUCTION 12 2.1 LOOP GROUPS 12 2.2 LOOP ALGEBRAS 13 2.3 DIFF S 1 AND G O X DIFF S 1 14 2.4 THE LIE ALGEBRAS 6 AND \| 8 16 2.5 CENTRAL EXTENSIONS OF GROUPS 17 2.6 CENTRAL EXTENSIONS OF LIE ALGEBRAS 19 2.7 H2(G, 2.8 H2(G,C) FOR G SIMPLE 24 2.9 A CENTRAL EXTENSION OF \| 8 26 2.10 INVARIANT BILINEAR FORMS 27 2.11 THE VIRASORO ALGEBRA 31 2.12 THE VIRASORO EXTENSION OF AFFINE ALGEBRAS 33 CHAPTER 3 STRUCTURE OF AFFINE ALGEBRAS 3.1 ROOT SPACE DECOMPOSITION OF G* 35 3.2 GENERATORS FOR G 37 3.3 TRIANGULAR DECOMPOSITION OF G AND G^ 40 3.4 CARTAN MATRIX AND DEFINING RELATIONS FOR G^ 41 3.5 INVOLUTIONS ON ^ 44 CHAPTER 4 REPRESENTATION THEORY 4.0 INTRODUCTION 46 4.1 REPRESENTATIONS AND MODULES 46 4.2 REDUCIBLE AND IRREDUCIBLE MODULES 47 4.3 INTCGRABLE REPRESENTATIONS 48 4.4 HIGHEST AND LOWEST WEIGHT MODULES 50 4.5 THE CONTRAVARIANT HERMITIAN FORM 54 CHAPTER 5 THE BASIC REPRESENTATION L(AQ) 5.0 INTRODUCTION 57 5.1 THE HOMOGENEOUS HCISENBERG SUBALGEBRA 57 5.2 THECENTRALIZERSOFS* 59 5.3 THE STRUCTURE OF Q(AQ) 63 5.4 VERTEX OPERATORS 65 5.5 THE PRINCIPAL REALIZATION OF L(AO) 69 CHAPTER 6 LIE ALGEBRAS OF INFINITE MATRICES 6.0 INTRODUCTION 72 6.1 THE LIE ALGEBRAS GL( ), SL(~ ) AND G (AOO) 72 6.2 THE CENTRE OF A KAC-MOODY ALGEBRA AND COMPLETIONS OF SL( ») T 76 6.3 CONNECTION WITH LOOP ALGEBRAS AND THEIR CENTRAL EXTENSIONS 83 6.4 REPRESENTATION THEORY OF SL(~) AND AOO 86 6.5 THE WEDGE REALIZATION OF L(AK)[KAC& PET 2J 88 6.6 THE BOSONIC REALIZATION OF L(A0 OVER A 94
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author	Bergvelt, Maarten J. Kroode, A. P. ten
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indexdate	2024-07-09T17:13:09Z
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language	English
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physical	97 S.
publishDate	1992
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publisher	Centrum voor Wiskunde en Informatica
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series	Centrum voor Wiskunde en Informatica <Amsterdam>: CWI syllabus
series2	Centrum voor Wiskunde en Informatica <Amsterdam>: CWI syllabus
spelling	Bergvelt, Maarten J. Verfasser aut Lectures on Kac-Moody algebras proceedings seminar 1986 - 1987 M. J. Bergvelt ; A. P. E. ten Kroode Amsterdam Centrum voor Wiskunde en Informatica 1992 97 S. txt rdacontent n rdamedia nc rdacarrier Centrum voor Wiskunde en Informatica <Amsterdam>: CWI syllabus 30 Kac-Moody-Algebra (DE-588)4223399-9 gnd rswk-swf (DE-588)1071861417 Konferenzschrift gnd-content Kac-Moody-Algebra (DE-588)4223399-9 s DE-604 Kroode, A. P. ten Verfasser aut Centrum voor Wiskunde en Informatica <Amsterdam>: CWI syllabus 30 (DE-604)BV002814804 30 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005282841&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Bergvelt, Maarten J. Kroode, A. P. ten Lectures on Kac-Moody algebras proceedings seminar 1986 - 1987 Centrum voor Wiskunde en Informatica <Amsterdam>: CWI syllabus Kac-Moody-Algebra (DE-588)4223399-9 gnd
subject_GND	(DE-588)4223399-9 (DE-588)1071861417
title	Lectures on Kac-Moody algebras proceedings seminar 1986 - 1987
title_auth	Lectures on Kac-Moody algebras proceedings seminar 1986 - 1987
title_exact_search	Lectures on Kac-Moody algebras proceedings seminar 1986 - 1987
title_full	Lectures on Kac-Moody algebras proceedings seminar 1986 - 1987 M. J. Bergvelt ; A. P. E. ten Kroode
title_fullStr	Lectures on Kac-Moody algebras proceedings seminar 1986 - 1987 M. J. Bergvelt ; A. P. E. ten Kroode
title_full_unstemmed	Lectures on Kac-Moody algebras proceedings seminar 1986 - 1987 M. J. Bergvelt ; A. P. E. ten Kroode
title_short	Lectures on Kac-Moody algebras
title_sort	lectures on kac moody algebras proceedings seminar 1986 1987
title_sub	proceedings seminar 1986 - 1987
topic	Kac-Moody-Algebra (DE-588)4223399-9 gnd
topic_facet	Kac-Moody-Algebra Konferenzschrift
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005282841&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV002814804
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