Classification and identification of Lie algebras:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, Rhode Island
American Mathematical Society
2014
|
| Schriftenreihe: | CRM monograph series
Volume 33 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | xi, 306 Seiten |
| ISBN: | 9780821843550 |
Internformat
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| 100 | 1 | |a Šnobl, Libor |d 1976- |e Verfasser |0 (DE-588)1054440905 |4 aut | |
| 245 | 1 | 0 | |a Classification and identification of Lie algebras |c Libor Snobl ; Pavel Winternitz |
| 264 | 1 | |a Providence, Rhode Island |b American Mathematical Society |c 2014 | |
| 300 | |a xi, 306 Seiten | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a CRM monograph series |v Volume 33 | |
| 500 | |a Includes bibliographical references and index | ||
| 650 | 0 | 7 | |a Lie-Algebra |0 (DE-588)4130355-6 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Lie-Algebra |0 (DE-588)4130355-6 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Winternitz, Pavel |d 1936- |e Verfasser |0 (DE-588)1063376998 |4 aut | |
| 830 | 0 | |a CRM monograph series |v Volume 33 |w (DE-604)BV007928388 |9 33 | |
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Datensatz im Suchindex
| _version_ | 1804175675240742912 |
|---|---|
| adam_text | Titel: Classification and identification of Lie algebras
Autor: Šnobl, Libor
Jahr: 2014
Contents
Preface ix
Acknowledgements xi
Part 1. General Theory 1
Chapter 1. Introduction and Motivation 3
Chapter 2. Basic Concepts 11
2.1. Definitions 11
2.2. Levi theorem 17
2.3. Classification of complex simple Lie algebras 17
2.4. Chevalley cohomology of Lie algebras 20
Chapter 3. Invariants of the Coadjoint Representation of a Lie Algebra 23
3.1. Casimir operators and generalized Casimir invariants 23
3.2. Calculation of generalized Casimir invariants using the infinitesimal
method 24
3.3. Calculation of generalized Casimir invariants by the method of
moving frames 32
Part 2. Recognition of a Lie Algebra Given by Its Structure
Constants 37
Chapter 4. Identification of Lie Algebras through the Use of Invariants 39
4.1. Elementary invariants 39
4.2. More sophisticated invariants 42
Chapter 5. Decomposition into a Direct Sum 47
5.1. General theory and criteria 47
5.2. Algorithm 56
5.3. Examples 57
Chapter 6. Levi Decomposition. Identification of the Radical and Levi
Factor 63
6.1. Original algorithm 63
6.2. Modified algorithm 65
6.3. Examples 66
Chapter 7. The Nilradical of a Lie Algebra 71
7.1. General theory 71
7.2. Algorithm 75
V
vi
CONTENTS
7.3. Examples 79
7.4. Identification of the nilradical using the Killing form 84
Part 3. Nilpotent, Solvable and Levi Decomposable Lie Algebras 87
Chapter 8. Nilpotent Lie Algebras 89
8.1. Maximal Abelian ideals and their extensions 89
8.2. Classification of low-dimensional nilpotent Lie algebras 93
Chapter 9. Solvable Lie Algebras and Their Nilradicals 99
9.1. General structure of a solvable Lie algebra 99
9.2. General procedure for classifying all solvable Lie algebras with a
given nilradical 99
9.3. Upper bound on the dimension of a solvable extension of a given
nilradical 103
9.4. Particular classes of nilradicals and their solvable extensions 105
9.5. Vector fields realizing bases of the coadjoint representation of a
solvable Lie algebra 106
Chapter 10. Solvable Lie Algebras with Abelian Nilradicals 107
10.1. Basic structural theorems 107
10.2. Decomposability properties of the solvable Lie algebras 114
10.3. Solvable Lie algebras with centers of maximal dimension 116
10.4. Solvable Lie algebras with one nonnilpotent element and an
n-dimensional Abelian nilradical 121
10.5. Solvable Lie algebras with two nonnilpotent elements and
n-dimensional Abelian nilradical 123
10.6. Generalized Casimir invariants of solvable Lie algebras with Abelian
nilradicals 125
Chapter 11. Solvable Lie Algebras with Heisenberg Nilradical 131
11.1. The Heisenberg relations and the Heisenberg algebra 131
11.2. Classification of solvable Lie algebras with nilradical f)(m) 132
11.3. The lowest dimensional case m — 1 134
11.4. The case m = 2 135
11.5. Generalized Casimir invariants 136
Chapter 12. Solvable Lie Algebras with Borei Nilradicals 141
12.1. Outer derivations of nilradicals of Borei subalgebras 141
12.2. Solvable extensions of the Borei nilradicals NR(b(g)) 146
12.3. Solvable Lie algebras with triangular nilradicals 153
12.4. Casimir invariants of nilpotent and solvable triangular Lie algebras 162
Chapter 13. Solvable Lie Algebras with Filiform and Quasifiliform Nilradicals 175
13.1. Classification of solvable Lie algebras with the model filiform
nilradical tin,i 176
13.2. Classification of solvable Lie algebras with the nilradical nn 2 182
13.3. Solvable Lie algebras with other filiform nilradicals 189
13.4. Example of an almost filiform nilradical 190
13.5. Generalized Casimir invariants of nrl,3 and of its solvable extensions 199
CONTENTS
vii
Chapter 14. Levi Decomposable Algebras 203
14.1. Levi decomposable algebras with a nilpotent radical 204
14.2. Levi decomposable algebras with nonnilpotent radicals 207
14.3. Levi decomposable algebras of low dimensions 208
Part 4. Low-Dimensional Lie Algebras 215
Chapter 15. Structure of the Lists of Low-Dimensional Lie Algebras 217
15.1. Ordering of the lists 217
15.2. Computer-assisted identification of a given Lie algebra 218
Chapter 16. Lie Algebras up to Dimension 3 225
16.1. One-dimensional Lie algebra 225
16.2. Solvable two-dimensional Lie algebra with the nilradical n^i 225
16.3. Nilpotent three-dimensional Lie algebra 225
16.4. Solvable three-dimensional Lie algebras with the nilradical 21^1 226
16.5. Simple three-dimensional Lie algebras 226
Chapter 17. Four-Dimensional Lie Algebras 227
17.1. Nilpotent four-dimensional Lie algebra 227
17.2. Solvable four-dimensional algebras with the nilradical 3ni i 227
17.3. Solvable four-dimensional Lie algebras with the nilradical n3,i 228
17.4. Solvable four-dimensional Lie algebras with the nilradical 2«!^ 229
Chapter 18. Five-Dimensional Lie Algebras 231
18.1. Nilpotent five-dimensional Lie algebras 231
18.2. Solvable five-dimensional Lie algebras with the nilradical 4ni,i 232
18.3. Solvable five-dimensional Lie algebras with the nilradical n3,i © n^i 235
18.4. Solvable five-dimensional Lie algebras with the nilradical n4ii 239
18.5. Solvable five dimensional Lie algebras with the nilradical 3t!!,! 240
18.6. Solvable five-dimensional Lie algebras with the nilradical 1x3,1 241
18.7. Five-dimensional Levi decomposable Lie algebra 241
Chapter 19. Six-Dimensional Lie Algebras 243
19.1. Nilpotent six-dimensional Lie algebras 243
19.2. Solvable six-dimensional Lie algebras with the nilradical 248
19.3. Solvable six-dimensional Lie algebras with the nilradical n3tj ©2^1253
19.4. Solvable six-dimensional Lie algebras with the nilradical n4 i © nxj 266
19.5. Solvable six-dimensional Lie algebras with the nilradical ns,i 271
19.6. Solvable six-dimensional Lie algebras with the nilradical n5j2 277
19.7. Solvable six-dimensional Lie algebras with the nilradical 115,3 279
19.8. Solvable six-dimensional Lie algebras with the nilradical n5i4 283
19.9. Solvable six-dimensional Lie algebras with the nilradical n5j5 285
19.10. Solvable six-dimensional Lie algebra with the nilradical tts^ 286
19.11. Solvable six-dimensional Lie algebras with the nilradical 4ni,i 286
19.12. Solvable six-dimensional Lie algebras with the nilradical 03,1 ©n^i 293
19.13. Solvable six-dimensional Lie algebra with the nilradical n4ii 296
19.14. Simple six-dimensional Lie algebra 296
19.15. Six-dimensional Levi decomposable Lie algebras 296
Bibliography
Index
CONTENTS
|
| any_adam_object | 1 |
| author | Šnobl, Libor 1976- Winternitz, Pavel 1936- |
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| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.482 |
| dewey-search | 512/.482 |
| dewey-sort | 3512 3482 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV043187511 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:20:03Z |
| institution | BVB |
| isbn | 9780821843550 |
| language | English |
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| physical | xi, 306 Seiten |
| publishDate | 2014 |
| publishDateSearch | 2014 |
| publishDateSort | 2014 |
| publisher | American Mathematical Society |
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| series | CRM monograph series |
| series2 | CRM monograph series |
| spelling | Šnobl, Libor 1976- Verfasser (DE-588)1054440905 aut Classification and identification of Lie algebras Libor Snobl ; Pavel Winternitz Providence, Rhode Island American Mathematical Society 2014 xi, 306 Seiten txt rdacontent n rdamedia nc rdacarrier CRM monograph series Volume 33 Includes bibliographical references and index Lie-Algebra (DE-588)4130355-6 gnd rswk-swf Lie-Algebra (DE-588)4130355-6 s DE-604 Winternitz, Pavel 1936- Verfasser (DE-588)1063376998 aut CRM monograph series Volume 33 (DE-604)BV007928388 33 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028611270&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Šnobl, Libor 1976- Winternitz, Pavel 1936- Classification and identification of Lie algebras CRM monograph series Lie-Algebra (DE-588)4130355-6 gnd |
| subject_GND | (DE-588)4130355-6 |
| title | Classification and identification of Lie algebras |
| title_auth | Classification and identification of Lie algebras |
| title_exact_search | Classification and identification of Lie algebras |
| title_full | Classification and identification of Lie algebras Libor Snobl ; Pavel Winternitz |
| title_fullStr | Classification and identification of Lie algebras Libor Snobl ; Pavel Winternitz |
| title_full_unstemmed | Classification and identification of Lie algebras Libor Snobl ; Pavel Winternitz |
| title_short | Classification and identification of Lie algebras |
| title_sort | classification and identification of lie algebras |
| topic | Lie-Algebra (DE-588)4130355-6 gnd |
| topic_facet | Lie-Algebra |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028611270&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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