Holdings: Essays in the history of lie groups and algebraic groups

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Title:	Essays in the history of lie groups and algebraic groups
From:	Armand Borel
Person:	Borel, Armand 1923-2003 Verfasser aut
Main Author:	Borel, Armand 1923-2003 (Author)
Format:	Book
Language:	English
Published:	Providence, RI American Mathematical Society 2001
Series:	History of mathematics 21
Notation:	SG 590 SK 340
Subjects:	Geschichte 1900-2000 Algebraïsche groepen Groupe de Lie Groupe linéaire algébrique Groupes linéaires algébriques - Histoire Histoire Lie, Groupes de - Histoire Lie-groepen Geschichte Lie groups > History Linear algebraic groups > History Lineare algebraische Gruppe Lie-Gruppe
Online Access:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009492671&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Physical Description:	XIII, 184 S. Ill.
ISBN:	0821802887

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adam_text	Contents Introduction ix Terminology for Classical Groups and Notation xi Photo Credits xiii Chapter I. Overview 1 Â§1. Lie s theory 1 Â§2. Lie algebras 5 Â§3. Globalizations 6 References for Chapter I 8 Chapter II. Full Reducibility and Invariants for SL2(C) 9 Â§1. Full reducibility, 1890 96 9 Â§2. Averaging. The invariant theorem 11 Â§3. Algebraic proofs of full reducibility 16 Â§4. Appendix: More on some proofs of full reducibility 18 References for Chapter II 26 Chapter III. Hermann Weyl and Lie Groups 29 Â§1. First contacts with Lie groups 29 Â§2. Representations of semisimple Lie groups and Lie algebras 31 Â§3. Impact on E. Cartan 35 Â§4. The Peter Weyl theorem. Harmonic analysis 37 Â§5. Group theory and quantum mechanics 38 Â§6. Representations and invariants of classical groups 40 Â§7. Two later developments 44 Notes 46 References for Chapter III 54 Chapter IV. Elie Cartan, Symmetric Spaces and Lie Groups 59 A. Building Up the Theory 60 Â§1. The spaces Â£. Local theory 60 Â§2. Spaces Â£ and semisimple groups. Global theory 64 Â§3. An exposition of Lie group theory from the global point of view 79 B. Further Developments 80 Â§4. Complete orthogonal systems on homogeneous spaces of compact Lie groups 80 viii CONTENTS Â§5. Differential forms and algebraic topology 84 Â§6. Bounded symmetric domains 88 References for Chapter IV 90 Chapter V. Linear Algebraic Groups in the 19th Century 93 Â§1. S. Lie, E. Study, and projective representations 93 Â§2. E. Study, Gordan series and linear representations of SL3 97 Â§3. Emile Picard 99 Â§4. Ludwig Maurer 102 Â§5. Elie Cartan 114 Â§6. Karl Carda 115 References for Chapter V 117 Chapter VI. Linear Algebraic Groups in the 20th Century 119 Â§1. Linear algebraic groups in characteristic zero. Replicas 119 Â§2. Groups over algebraically closed ground fields I 119 Â§3. Groups over an algebraically closed ground field II 124 Â§4. Rationality properties 126 Â§5. Algebraic groups and geometry. Tits systems and Tits buildings 131 Â§6. Abstract automorphisms 134 Â§7. Merger 142 References for Chapter VI 144 Chapter VII. The Work of Chevalley in Lie Groups and Algebraic Groups 147 Â§1. Lie groups, 1941 1946 147 Â§2. Linear algebraic groups, 1943 1951 150 Â§3. Lie groups, 1948 1955 152 Â§4. Linear algebraic groups, 1954 155 Â§5. Algebraic groups. 1955 1961 156 References for Chapter VII 162 Chapter VIII. Algebraic Groups and Galois Theory in the Work of Ellis R. Kolchin 165 Â§1. The Picard Vessiot theory 165 Â§2. Linear algebraic groups 169 Â§3. Generalization of the Picard Vessiot theory 170 Â§4. Galois theory of strongly normal extensions 173 Â§5. Foundational work on algebraic sets and groups 176 References for Chapter VIII 179 Name Index 181 Subject Index 183
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spellingShingle	Borel, Armand 1923-2003 Essays in the history of lie groups and algebraic groups History of mathematics Algebraïsche groepen gtt Groupe de Lie rasuqam Groupe linéaire algébrique rasuqam Groupes linéaires algébriques - Histoire Histoire rasuqam Lie, Groupes de - Histoire Lie-groepen gtt Geschichte Lie groups History Linear algebraic groups History Lineare algebraische Gruppe (DE-588)4295326-1 gnd Lie-Gruppe (DE-588)4035695-4 gnd
subject_GND	(DE-588)4295326-1 (DE-588)4035695-4
title	Essays in the history of lie groups and algebraic groups
title_auth	Essays in the history of lie groups and algebraic groups
title_exact_search	Essays in the history of lie groups and algebraic groups
title_full	Essays in the history of lie groups and algebraic groups Armand Borel
title_fullStr	Essays in the history of lie groups and algebraic groups Armand Borel
title_full_unstemmed	Essays in the history of lie groups and algebraic groups Armand Borel
title_short	Essays in the history of lie groups and algebraic groups
title_sort	essays in the history of lie groups and algebraic groups
topic	Algebraïsche groepen gtt Groupe de Lie rasuqam Groupe linéaire algébrique rasuqam Groupes linéaires algébriques - Histoire Histoire rasuqam Lie, Groupes de - Histoire Lie-groepen gtt Geschichte Lie groups History Linear algebraic groups History Lineare algebraische Gruppe (DE-588)4295326-1 gnd Lie-Gruppe (DE-588)4035695-4 gnd
topic_facet	Algebraïsche groepen Groupe de Lie Groupe linéaire algébrique Groupes linéaires algébriques - Histoire Histoire Lie, Groupes de - Histoire Lie-groepen Geschichte Lie groups History Linear algebraic groups History Lineare algebraische Gruppe Lie-Gruppe
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009492671&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV001327576
work_keys_str_mv	AT borelarmand essaysinthehistoryofliegroupsandalgebraicgroups

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Holdings details from UB Handapparat Mathematik Prof. Friedl 1
Call Number:	8019 SK 340 B731 E7
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