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Titel:	The recognition theorem for graded Lie algebras in prime characteristic
Von:	Georgia Benkart ; Thomas Gregory ; Alexander Premet
Person:	Benkart, Georgia 1949-2022 Verfasser aut Gregory, Thomas Bradford Premet, Alexander 1944- 1955- Sonstige
Hauptverfasser:	Benkart, Georgia 1949-2022 (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	Providence, RI American Math. Soc. 2009
Schriftenreihe:	Memoirs of the American Mathematical Society 920
Schlagwörter:	Lie algebras Lie-Algebra
Medienzugang:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017126277&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Beschreibung:	"Volume 197, number 920 (second of 5 numbers)." Includes bibliographical references
Umfang:	XI, 145 S.
ISBN:	9780821842263

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MARC


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Datensatz im Suchindex

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adam_text	Titel: The recognition theorem for graded Lie algebras in prime characteristic Autor: Benkart, Georgia Jahr: 2009 Contents Introduction ix Chapter 1. Graded Lie Algebras 1 1.1. Introduction 1 1.2. The Weisfeiler radical 2 1.3. The minimal ideal 3 4 1.4. The graded algebras B(V-t) and B{Vt) 5 1.5. The local subalgebra 8 1.6. General properties of graded Lie algebras 9 1.7. Restricted Lie algebras 15 1.8. The main theorem on restrictedness (Theorem 1.63) 17 1.9. Remarks on restrictedness 17 1.10. The action of go on g_j 18 1.11. The depth-one case of Theorem 1.63 20 1.12. Proof of Theorem 1.63 in the depth-one case 21 1.13. Quotients of go 22 1.14. The proof of Theorem 1.63 when 2 q r 24 1.15. The proof of Theorem 1.63 when q r 25 1.16. General setup 25 1.17. The assumption [[g_i,fli],fli] ^ 0 in Theorem 1.63 30 Chapter 2. Simple Lie Algebras and Algebraic Groups 31 2.1. Introduction 31 2.2. General information about the classical Lie algebras 31 2.3. Representations of algebraic groups 38 2.4. Standard gradings of classical Lie algebras 41 2.5. The Lie algebras of Cartan type 42 2.6. The Jacobson-Witt algebras 43 2.7. Divided power algebras 44 2.8. Witt Lie algebras of Cartan type (the W series) 45 2.9. Special Lie algebras of Cartan type (the S series) 47 2.10. Hamiltonian Lie algebras of Cartan type (the H series) 50 2.11. Contact Lie algebras of Cartan type (the K series) 54 2.12. The Recognition Theorem with stronger hypotheses 56 2.13. gi as a go-module for Lie algebras g of Cartan type 57 2.14. Melikyan Lie algebras 66 vi CONTENTS Chapter 3. The Contragredient Case 69 3.1. Introduction 69 3.2. Results on modules for three-dimensional Lie algebras 69 3.3. Primitive vectors in g± and g_i 74 3.4. Subalgebras with a balanced grading 77 3.5. Algebras with an unbalanced grading 86 Chapter 4. The Noncontragredient Case 97 4.1. General assumptions and notation 97 4.2. Brackets of weight vectors in opposite gradation spaces 98 4.3. Determining flo an(i its representation on Q—± 99 4.4. Additional assumptions 105 4.5. Computing weights of b~-primitive vectors in Qx 105 4.6. Determination of the local Lie algebra 115 4.7. The irreducibility of 0X 125 4.8. Determining the negative part when jji is irreducible 133 4.9. Determining the negative part when Qi is reducible 137 4.10. The case that go is abelian 141 4.11. Completion of the proof of the Main Theorem 142 Bibliography 143
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indexdate	2024-12-20T13:28:30Z
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isbn	9780821842263
language	English
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physical	XI, 145 S.
publishDate	2009
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publisher	American Math. Soc.
record_format	marc
series	Memoirs of the American Mathematical Society
series2	Memoirs of the American Mathematical Society
spellingShingle	Benkart, Georgia 1949-2022 The recognition theorem for graded Lie algebras in prime characteristic Memoirs of the American Mathematical Society Lie algebras Lie-Algebra (DE-588)4130355-6 gnd
subject_GND	(DE-588)4130355-6
title	The recognition theorem for graded Lie algebras in prime characteristic
title_auth	The recognition theorem for graded Lie algebras in prime characteristic
title_exact_search	The recognition theorem for graded Lie algebras in prime characteristic
title_full	The recognition theorem for graded Lie algebras in prime characteristic Georgia Benkart ; Thomas Gregory ; Alexander Premet
title_fullStr	The recognition theorem for graded Lie algebras in prime characteristic Georgia Benkart ; Thomas Gregory ; Alexander Premet
title_full_unstemmed	The recognition theorem for graded Lie algebras in prime characteristic Georgia Benkart ; Thomas Gregory ; Alexander Premet
title_short	The recognition theorem for graded Lie algebras in prime characteristic
title_sort	the recognition theorem for graded lie algebras in prime characteristic
topic	Lie algebras Lie-Algebra (DE-588)4130355-6 gnd
topic_facet	Lie algebras Lie-Algebra
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017126277&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV008000141
work_keys_str_mv	AT benkartgeorgia therecognitiontheoremforgradedliealgebrasinprimecharacteristic AT gregorythomasbradford therecognitiontheoremforgradedliealgebrasinprimecharacteristic AT premetalexander therecognitiontheoremforgradedliealgebrasinprimecharacteristic

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Exemplar 1	entleihbar Vorhanden Dieser Titel ist mit anderen zusammengebunden. Bitte bestellen Sie folgenden: Sum formula for SL 2 over a totally real number field Inhalt Folgende Werke befinden sich in dem Buch mit der oben genannten Signatur. Sum formula for SL 2 over a totally real number field The recognition theorem for graded Lie algebras in prime characteristic Compactification of the Drinfeld modular surfaces Asymptotic expansions for infinite weighted convolutions of heavy tail distributions... Minimal resolutions via algebraic discrete morse theory