The recognition theorem for graded Lie algebras in prime characteristic:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
American Math. Soc.
2009
|
| Series: | Memoirs of the American Mathematical Society
920 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | "Volume 197, number 920 (second of 5 numbers)." Includes bibliographical references |
| Physical Description: | XI, 145 S. |
| ISBN: | 9780821842263 |
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| 245 | 1 | 0 | |a The recognition theorem for graded Lie algebras in prime characteristic |c Georgia Benkart ; Thomas Gregory ; Alexander Premet |
| 264 | 1 | |a Providence, RI |b American Math. Soc. |c 2009 | |
| 300 | |a XI, 145 S. | ||
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| 490 | 1 | |a Memoirs of the American Mathematical Society |v 920 | |
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| 500 | |a Includes bibliographical references | ||
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Record in the Search Index
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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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| id | DE-604.BV035321710 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T21:31:15Z |
| institution | BVB |
| isbn | 9780821842263 |
| language | English |
| lccn | 2008039455 |
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| physical | XI, 145 S. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | American Math. Soc. |
| record_format | marc |
| series | Memoirs of the American Mathematical Society |
| series2 | Memoirs of the American Mathematical Society |
| spelling | Benkart, Georgia 1949-2022 Verfasser (DE-588)112708048 aut The recognition theorem for graded Lie algebras in prime characteristic Georgia Benkart ; Thomas Gregory ; Alexander Premet Providence, RI American Math. Soc. 2009 XI, 145 S. txt rdacontent n rdamedia nc rdacarrier Memoirs of the American Mathematical Society 920 "Volume 197, number 920 (second of 5 numbers)." Includes bibliographical references Lie algebras Lie-Algebra (DE-588)4130355-6 gnd rswk-swf Lie-Algebra (DE-588)4130355-6 s DE-604 Gregory, Thomas Bradford 1944- Sonstige (DE-588)137963130 oth Premet, Alexander 1955- Sonstige (DE-588)114927766 oth Memoirs of the American Mathematical Society 920 (DE-604)BV008000141 920 HBZ Datenaustausch application/pdf 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 Inhaltsverzeichnis |
| 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 |
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