Availability: Some generalized Kac-Moody algebras with known root multiplicities

Some generalized Kac-Moody algebras with known root multiplicities:

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Bibliographic Details
Main Author:	Niemann, Peter (Author)
Format:	Book
Language:	English
Published:	Providence, RI AMS 2002
Series:	Memoirs of the American Mathematical Society 746
Subjects:	Kac-Moody algebras Root systems (Algebra) Kac-Moody-Algebra
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009827168&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Item Description:	"Volume 157, number 746 (second of 5 numbers)."
Physical Description:	IX, 119 S. graph. Darst.
ISBN:	0821828886

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Record in the Search Index

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adam_text	OF THE AMERICAN MATHEMATICAL SOCIETY NUMBER 746 SOME GENERALIZED KAC-MOODY ALGEBRAS WITH KNOWN ROOT MULTIPLICITIES PETER NIEMANN LS EM. MAY 2002 * VOLUME 157 * NUMBER 746 (SECOND OF 5 NUMBERS) * ISSN 0065-9266 AMERICAN MATHEMATICAL SOCIETY PROVIDENCE, RHODE ISLAND CONTENTS INTRODUCTION 1 CHAPTER 1. GENERALIZED KAC-MOODY ALGEBRAS 5 1.1. DEFINITION AND FUNDAMENTAL PROPERTIES 5 1.2. THE DENOMINATOR FORMULA 9 1.3. VERTEX ALGEBRAS 11 1.4. THE FAKE MONSTER LIE ALGEBRA 15 1.5. THE TWISTED DENOMINATOR FORMULA 18 1.6. CONSTRUCTION OF THE GKMS 20 1.7. ROOT MULTIPLICITIES 24 CHAPTER 2. MODULAR FORMS 29 2.1. REVIEW OF MODULAR GROUP AND MODULAR FORMS 29 2.2. SOME MODULAR FORMS RELATED TO ETA 31 CHAPTER 3. LATTICES AND THEIR THETA-FUNCTIONS 34 3.1. REVIEW OF RESULTS ABOUT LATTICES 34 3.2. THE CHARACTER OF THETA 35 CHAPTER 4. THE PROOF OF THEOREM 1.7 38 4.1. THE THETA-FUNCTION OF L* 38 4.2. SUMS OF QUADRATIC RESIDUES 44 4.3. THE SHORT VECTORS OF L* 46 4.4. THE CONCLUSION OF THE PROOF 49 CHAPTER 5. THE REAL SIMPLE ROOTS 54 5.1. THE SET OF REAL SIMPLE ROOTS 54 5.2. HOLES AND DYNKIN DIAGRAMS 56 5.3. THE VOLUME FORMULA 63 5.4. THE AUTOMORPHISM GROUPS 67 CHAPTER 6. HYPERBOLIC LIE ALGEBRAS 72 6.1. WAN S CLASSIFICATION 73 6.2. FINITE, AFFINE, AND HYPERBOLIC SUBALGEBRAS 73 6.3. CONCLUSIONS 89 APPENDIX A 93 N=23 93 N=LL 94 N=7 94 N=5 95 VIII CONTENTS N=3 96 N=2 99 APPENDIX B 110 BIBLIOGRAPHY 116 NOTATION 118
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spellingShingle	Niemann, Peter Some generalized Kac-Moody algebras with known root multiplicities Memoirs of the American Mathematical Society Kac-Moody algebras Root systems (Algebra) Kac-Moody-Algebra (DE-588)4223399-9 gnd
subject_GND	(DE-588)4223399-9
title	Some generalized Kac-Moody algebras with known root multiplicities
title_auth	Some generalized Kac-Moody algebras with known root multiplicities
title_exact_search	Some generalized Kac-Moody algebras with known root multiplicities
title_full	Some generalized Kac-Moody algebras with known root multiplicities Peter Niemann
title_fullStr	Some generalized Kac-Moody algebras with known root multiplicities Peter Niemann
title_full_unstemmed	Some generalized Kac-Moody algebras with known root multiplicities Peter Niemann
title_short	Some generalized Kac-Moody algebras with known root multiplicities
title_sort	some generalized kac moody algebras with known root multiplicities
topic	Kac-Moody algebras Root systems (Algebra) Kac-Moody-Algebra (DE-588)4223399-9 gnd
topic_facet	Kac-Moody algebras Root systems (Algebra) Kac-Moody-Algebra
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009827168&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV008000141
work_keys_str_mv	AT niemannpeter somegeneralizedkacmoodyalgebraswithknownrootmultiplicities

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