Modular Lie algebras and their representations:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York u.a.
Dekker
1988
|
| Edition: | 1. print. |
| Series: | Pure and applied mathematics
116. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VIII, 301 S. |
| ISBN: | 0824775945 |
Staff View
MARC
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| 100 | 1 | |a Strade, Helmut |d 1942- |e Verfasser |0 (DE-588)106816659 |4 aut | |
| 245 | 1 | 0 | |a Modular Lie algebras and their representations |c Helmut Strade ; Rolf Farnsteiner |
| 250 | |a 1. print. | ||
| 264 | 1 | |a New York u.a. |b Dekker |c 1988 | |
| 300 | |a VIII, 301 S. | ||
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Record in the Search Index
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| adam_text | Contents
PREFACE iii
CHAPTER 1 CLASSICAL THEORY 1
1.1 Basic Definitions of Lie Algebras and
Representations 1
1.2 Some Basic Module Operations 11
1.3 Nilpotent Lie Algebras; Engel s Theorem 14
1.4 Primary Decomposition; Cartan Subalgebras 22
1.5 Solvable Lie Algebras; Lie s Theorem 28
1.6 Examples of Low Dimension 33
1.7 The Solvable Radical and Cartan s
Criterion for Solvability 38
1.8 The Universal Enveloping Algebra 44
1.9 Filtrations 52
References 60
CHAPTER 2 BASIC THEORY OF RESTRICTABLE LIE ALGEBRAS 61
2.1 p Mappings and Restricted Lie Algebras 61
2.2 Existence of p Mappings; Restrictable
Lie Algebras 70
2.3 Some Properties of the p Mapping 77
2.4 Tori and Cartan Decomposition 85
2.5 Restricted Enveloping Algebras and
Universal p Envelopes 90
References 98
CHAPTER 3 FILTERED AND GRADED LIE ALGEBRAS 99
3.1 Filtered Lie Algebras 100
3.2 Graded Lie Algebras 107
3.3 The Interrelation Between Filtrations
and Gradations; Criteria for Simplicity 111
3.4 Subsidiary Results on Filtrations and
Gradations 118
3.5 Realizations as Derivation Algebras 124
References 140
vii
viii Contents
CHAPTER 4 GRADED LIE ALGEBRAS OF CARTAN TYPE 141
4.1 The Construction Processes 141
4.2 The Generalized Jacobson Witt Algebra
W(n;m) 146
4.3 The Special Algebra S(n;m) 153
4.4 The Hamiltonian Algebra H(2r;m) 162
4.5 The Contact Algebra K(2r + l;~m) 169
4.6 Associative Forms of Graded Cartan
Type Lie Algebras 178
4.7 Generators of Restricted Cartan Type
Lie Algebras 186
4.8 The Derivation Algebras of the Restricted
Cartan Type Lie Algebras 191
References 200
CHAPTER 5 REPRESENTATIONS OF MODULAR LIE ALGEBRAS 201
5.1 The Center of the Universal Enveloping
Algebra 201
5.2 Irreducible Representations 205
5.3 Reduced Enveloping Algebras 212
5.4 Frobenius Algebras 215
5.5 Lie Algebras with Completely Reducible
Representations 219
5.6 Induced Representations 224
5.7 A Criterion for Irreducibility 229
5.8 Representations of Solvable Lie Algebras 237
5.9 Examples 244
References 248
CHAPTER 6 THE IDEAL STRUCTURE OF THE UNIVERSAL
ENVELOPING ALGEBRA 249
6.1 The Prime Spectrum of a Ring 249
6.2 Noetherian Rings 249
6.3 Properties of the Mapping
Spec(A) Spec(R) 257
6.4 The Going Down Property 262
6.5 The Prime Spectrum of U(L) 264
6.6 The Maximal Dimension of Irreducible
Modules 272
6.7 Examples 275
References 278
NOTATION 281
BIBLIOGRAPHY 281
INDEX 299
|
| any_adam_object | 1 |
| author | Strade, Helmut 1942- Farnsteiner, Rolf |
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| ctrlnum | (OCoLC)16581936 (DE-599)BVBBV005791472 |
| dewey-full | 512/.55 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.55 |
| dewey-search | 512/.55 |
| dewey-sort | 3512 255 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. print. |
| format | Book |
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| id | DE-604.BV005791472 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:34:44Z |
| institution | BVB |
| isbn | 0824775945 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-003619055 |
| oclc_num | 16581936 |
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| owner_facet | DE-703 DE-824 DE-19 DE-BY-UBM DE-12 DE-91G DE-BY-TUM DE-384 DE-739 DE-29T DE-706 |
| physical | VIII, 301 S. |
| publishDate | 1988 |
| publishDateSearch | 1988 |
| publishDateSort | 1988 |
| publisher | Dekker |
| record_format | marc |
| series | Pure and applied mathematics |
| series2 | Pure and applied mathematics |
| spelling | Strade, Helmut 1942- Verfasser (DE-588)106816659 aut Modular Lie algebras and their representations Helmut Strade ; Rolf Farnsteiner 1. print. New York u.a. Dekker 1988 VIII, 301 S. txt rdacontent n rdamedia nc rdacarrier Pure and applied mathematics 116. Algèbre Lie modulaire Algèbre enveloppante Lie, Algèbres de ram Modules (algèbre) ram Représentation algèbre Lie Représentations d'algèbres ram Lie algebras Modules (Algebra) Representations of algebras Modul (DE-588)4129770-2 gnd rswk-swf Darstellungstheorie (DE-588)4148816-7 gnd rswk-swf Lie-Algebra (DE-588)4130355-6 gnd rswk-swf Lie-Algebra (DE-588)4130355-6 s Darstellungstheorie (DE-588)4148816-7 s DE-604 Modul (DE-588)4129770-2 s Farnsteiner, Rolf Verfasser aut Pure and applied mathematics 116. (DE-604)BV000001885 116 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003619055&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Strade, Helmut 1942- Farnsteiner, Rolf Modular Lie algebras and their representations Pure and applied mathematics Algèbre Lie modulaire Algèbre enveloppante Lie, Algèbres de ram Modules (algèbre) ram Représentation algèbre Lie Représentations d'algèbres ram Lie algebras Modules (Algebra) Representations of algebras Modul (DE-588)4129770-2 gnd Darstellungstheorie (DE-588)4148816-7 gnd Lie-Algebra (DE-588)4130355-6 gnd |
| subject_GND | (DE-588)4129770-2 (DE-588)4148816-7 (DE-588)4130355-6 |
| title | Modular Lie algebras and their representations |
| title_auth | Modular Lie algebras and their representations |
| title_exact_search | Modular Lie algebras and their representations |
| title_full | Modular Lie algebras and their representations Helmut Strade ; Rolf Farnsteiner |
| title_fullStr | Modular Lie algebras and their representations Helmut Strade ; Rolf Farnsteiner |
| title_full_unstemmed | Modular Lie algebras and their representations Helmut Strade ; Rolf Farnsteiner |
| title_short | Modular Lie algebras and their representations |
| title_sort | modular lie algebras and their representations |
| topic | Algèbre Lie modulaire Algèbre enveloppante Lie, Algèbres de ram Modules (algèbre) ram Représentation algèbre Lie Représentations d'algèbres ram Lie algebras Modules (Algebra) Representations of algebras Modul (DE-588)4129770-2 gnd Darstellungstheorie (DE-588)4148816-7 gnd Lie-Algebra (DE-588)4130355-6 gnd |
| topic_facet | Algèbre Lie modulaire Algèbre enveloppante Lie, Algèbres de Modules (algèbre) Représentation algèbre Lie Représentations d'algèbres Lie algebras Modules (Algebra) Representations of algebras Modul Darstellungstheorie Lie-Algebra |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003619055&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000001885 |
| work_keys_str_mv | AT stradehelmut modularliealgebrasandtheirrepresentations AT farnsteinerrolf modularliealgebrasandtheirrepresentations |