Lie algebras:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English Chinese |
| Published: |
Oxford [u.a.]
Pergamon Pr.
1975
|
| Edition: | 1. ed. |
| Series: | International series of monographs in pure and applied mathematics
104 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Einheitssacht.: Li tai shu <engl.> |
| Physical Description: | VII, 231 S. |
| ISBN: | 0080179525 |
Staff View
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| 245 | 1 | 0 | |a Lie algebras |
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| 264 | 1 | |a Oxford [u.a.] |b Pergamon Pr. |c 1975 | |
| 300 | |a VII, 231 S. | ||
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| 490 | 1 | |a International series of monographs in pure and applied mathematics |v 104 | |
| 500 | |a Einheitssacht.: Li tai shu <engl.> | ||
| 650 | 7 | |a Lie, Groupes de |2 ram | |
| 650 | 4 | |a Lie algebras | |
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Record in the Search Index
| _version_ | 1804135986235441152 |
|---|---|
| adam_text | CONTENTS
Preface vii
1. Basic concepts l
1.1. Lie algebras 1
1.2. Subalgebras, ideals and quotient algebras 4
1.3. Simple algebras 7
1.4. Direct sum 11
1.5. Derived series and descending central series 12
1.6. Killing form 16
2. Nilpotent and solvable Lie algebras 21
2.1. Preliminaries 21
2.2. Engel s theorem 22
2.3. Lie s theorem 24
2.4. Nilpotent linear Lie algebras 26
3. Cartan subalgebras 31
3.1. Cartan subalgebras 31
3.2. Existence of Cartan subalgebras 34
3.3. Preliminaries 36
3.4. Conjugacy of Cartan subalgebras 41
4. Cartan s criterion 44
4.1. Preliminaries 44
4.2. Cartan s criterion for solvable Lie algebras 45
4.3. Cartan s criterion for semisimple Lie algebras 47
5. Cartan decompositions and root systems of semisimple Lie algebras 48
5.1. Cartan decompositions of semisimple Lie algebras 48
5.2. Root systems of semisimple Lie algebras 53
5.3. Dependence of structure of semisimple Lie algebras on root systems 58
5.4. Root systems of the classical Lie algebras 66
6. Fundamental systems of roots of semisimple Lie algebras and Weyl groups 74
6.1. Fundamental systems of roots and prime roots 74
6.2. Fundamental systems of roots of the classical Lie algebras 80
6.3. Weyl groups 82
6.4. Properties of Weyl groups 86
7. Classification of simple Lie algebras 92
7.1. Diagrams of n systems 92
7.2. Classification of simple n systems 93
7.3. The Lie algebra G2 100
7.4. Classification of simple Lie algebras 102
V
vi CONTENTS
8. Automorphisms of semisimple Lie algebras 105
8.1. The group of automorphisms and the derivation algebra of a Lie algebra 105
8.2. The group of outer automorphisms of a semisimple Lie algebra 108
9. Representations of Lie algebras 116
9.1. Fundamental concepts 116
9.2. Schur s lemma 119
9.3. Representations of the three dimensional simple Lie algebra 120
10. Representations of semisimple Lie algebras 126
10.1. Irreducible representations of semisimple Lie algebras 126
10.2. Theorem of complete reducibility 134
10.3. Fundamental representations of semisimple Lie algebras 142
10.4. Tensor representations 145
10.5. Elementary representations of simple Lie algebras 148
11. Representations of the classical Lie algebras 151
11.1. Representations of An 151
11.2. Representations of Cn 155
11.3. Representations of Bn 156
11.4. Representations of A. 58
12. Spin representations and the exceptional Lie algebras 160
12.1. Associative algebras 160
12.2. Clifford algebra 161
12.3. Spin representations 165
12.4. The exceptional Lie algebras F4 and Eg 168
13. Poincare Birkhoff Witt theorem and its applications to representation theory of
semisimple Lie algebras I80
13.1. Enveloping algebras of Lie algebras 180
13.2. Poincare—Birkhoff— Witt theorem 182
13.3. Applications to representations of semisimple Lie algebras 188
14. Characters of irreducible representations of semisimple Lie algebras 190
14.1. A recursion formula for the multiplicity of a weight of an irreducible represen¬
tation 190
14.2. Half of the sum of all the positive roots 197
14.3. Alternating functions 200
14.4. Formula of the character of an irreducible representation 203
15. Real forms of complex semisimple Lie algebras 210
15.1. Complex extension of real Lie algebras and real forms of complex Lie algebras 210
15.2. Compact Lie algebras 212
15.3. Compact real forms of complex semisimple Lie algebras 215
15.4. Roots and weights of compact semisimple Lie algebras 221
15.5. Real forms of complex semisimple Lie algebras 223
Index 227
Other Titles in the Series in Pure and Applied Mathematics 229
|
| adam_txt |
CONTENTS
Preface vii
1. Basic concepts l
1.1. Lie algebras 1
1.2. Subalgebras, ideals and quotient algebras 4
1.3. Simple algebras 7
1.4. Direct sum 11
1.5. Derived series and descending central series 12
1.6. Killing form 16
2. Nilpotent and solvable Lie algebras 21
2.1. Preliminaries 21
2.2. Engel's theorem 22
2.3. Lie's theorem 24
2.4. Nilpotent linear Lie algebras 26
3. Cartan subalgebras 31
3.1. Cartan subalgebras 31
3.2. Existence of Cartan subalgebras 34
3.3. Preliminaries 36
3.4. Conjugacy of Cartan subalgebras 41
4. Cartan's criterion 44
4.1. Preliminaries 44
4.2. Cartan's criterion for solvable Lie algebras 45
4.3. Cartan's criterion for semisimple Lie algebras 47
5. Cartan decompositions and root systems of semisimple Lie algebras 48
5.1. Cartan decompositions of semisimple Lie algebras 48
5.2. Root systems of semisimple Lie algebras 53
5.3. Dependence of structure of semisimple Lie algebras on root systems 58
5.4. Root systems of the classical Lie algebras 66
6. Fundamental systems of roots of semisimple Lie algebras and Weyl groups 74
6.1. Fundamental systems of roots and prime roots 74
6.2. Fundamental systems of roots of the classical Lie algebras 80
6.3. Weyl groups 82
6.4. Properties of Weyl groups 86
7. Classification of simple Lie algebras 92
7.1. Diagrams of n systems 92
7.2. Classification of simple n systems 93
7.3. The Lie algebra G2 100
7.4. Classification of simple Lie algebras 102
V
vi CONTENTS
8. Automorphisms of semisimple Lie algebras 105
8.1. The group of automorphisms and the derivation algebra of a Lie algebra 105
8.2. The group of outer automorphisms of a semisimple Lie algebra 108
9. Representations of Lie algebras 116
9.1. Fundamental concepts 116
9.2. Schur's lemma 119
9.3. Representations of the three dimensional simple Lie algebra 120
10. Representations of semisimple Lie algebras 126
10.1. Irreducible representations of semisimple Lie algebras 126
10.2. Theorem of complete reducibility 134
10.3. Fundamental representations of semisimple Lie algebras 142
10.4. Tensor representations 145
10.5. Elementary representations of simple Lie algebras 148
11. Representations of the classical Lie algebras 151
11.1. Representations of An 151
11.2. Representations of Cn 155
11.3. Representations of Bn 156
11.4. Representations of A. '58
12. Spin representations and the exceptional Lie algebras 160
12.1. Associative algebras 160
12.2. Clifford algebra 161
12.3. Spin representations 165
12.4. The exceptional Lie algebras F4 and Eg 168
13. Poincare Birkhoff Witt theorem and its applications to representation theory of
semisimple Lie algebras I80
13.1. Enveloping algebras of Lie algebras 180
13.2. Poincare—Birkhoff— Witt theorem 182
13.3. Applications to representations of semisimple Lie algebras 188
14. Characters of irreducible representations of semisimple Lie algebras 190
14.1. A recursion formula for the multiplicity of a weight of an irreducible represen¬
tation 190
14.2. Half of the sum of all the positive roots 197
14.3. Alternating functions 200
14.4. Formula of the character of an irreducible representation 203
15. Real forms of complex semisimple Lie algebras 210
15.1. Complex extension of real Lie algebras and real forms of complex Lie algebras 210
15.2. Compact Lie algebras 212
15.3. Compact real forms of complex semisimple Lie algebras 215
15.4. Roots and weights of compact semisimple Lie algebras 221
15.5. Real forms of complex semisimple Lie algebras 223
Index 227
Other Titles in the Series in Pure and Applied Mathematics 229 |
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| illustrated | Not Illustrated |
| index_date | 2024-07-02T16:11:50Z |
| indexdate | 2024-07-09T20:49:13Z |
| institution | BVB |
| isbn | 0080179525 |
| language | English Chinese |
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| physical | VII, 231 S. |
| publishDate | 1975 |
| publishDateSearch | 1975 |
| publishDateSort | 1975 |
| publisher | Pergamon Pr. |
| record_format | marc |
| series | International series of monographs in pure and applied mathematics |
| series2 | International series of monographs in pure and applied mathematics |
| spelling | Wan, Zhexian 1927- Verfasser (DE-588)132646943 aut Lie algebras 1. ed. Oxford [u.a.] Pergamon Pr. 1975 VII, 231 S. txt rdacontent n rdamedia nc rdacarrier International series of monographs in pure and applied mathematics 104 Einheitssacht.: Li tai shu <engl.> Lie, Groupes de ram Lie-Algebra (DE-588)4130355-6 gnd rswk-swf Lie-Algebra (DE-588)4130355-6 s DE-604 International series of monographs in pure and applied mathematics 104 (DE-604)BV001888024 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015226372&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Wan, Zhexian 1927- Lie algebras International series of monographs in pure and applied mathematics Lie, Groupes de ram Lie algebras Lie-Algebra (DE-588)4130355-6 gnd |
| subject_GND | (DE-588)4130355-6 |
| title | Lie algebras |
| title_auth | Lie algebras |
| title_exact_search | Lie algebras |
| title_exact_search_txtP | Lie algebras |
| title_full | Lie algebras |
| title_fullStr | Lie algebras |
| title_full_unstemmed | Lie algebras |
| title_short | Lie algebras |
| title_sort | lie algebras |
| topic | Lie, Groupes de ram Lie algebras Lie-Algebra (DE-588)4130355-6 gnd |
| topic_facet | Lie, Groupes de Lie algebras Lie-Algebra |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015226372&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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