The theory of Lie superalgebras: an introduction
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
1979
|
| Series: | Lecture notes in mathematics
716 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 271 S. |
| ISBN: | 3540092560 0387092560 |
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MARC
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| 100 | 1 | |a Scheunert, Manfred |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a The theory of Lie superalgebras |b an introduction |c Manfred Scheunert |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1979 | |
| 300 | |a X, 271 S. | ||
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Record in the Search Index
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| adam_text | Table of contents
Introduction 1
Chapter 0 Preparatory remarks 5
§1 Conventions 5
§2 Some general remarks on graded algebraic structures 6
Chapter I Formal constructions 12
§1 Definition and elementary properties of Lie superalgebras 12
§2 The enveloping algebra of a Lie superalgebra 19
1. Definition and some basic properties of the enveloping algebra 19
2. The supersymmetric algebra of a graded vector space 23
3. Filtration of the enveloping algebra and the Poincare, Birk-
hoff, Witt theorem 25
4. The enveloping algebra as a Hopf superalgebra 31
§3 Representations of Lie superalgebras 34
1. The connection between representations of L and U(L) 34
2. Canonical constructions with L -modules 37
A. Extension of the base field 37
B. The tensor product of graded L-modules 38
C. Representations in spaces of multilinear mappings 41
3. Invariants 45
§4 Induced and produced representations 51
1. Induced representations 52
2. Produced representations 54
3. Additional structures on produced modules : Filtration and
multiplication 56
4. Some non-canonical constructions 60
5. The Guillemin, Sternberg realization theorem 62
Chapter II Simple Lie superalgebras 72
§1 Miscellanies on Z - graded and filtered Lie superalgebras 72
1. Some definitions concerning Z - graded Lie superalgebras and
a criterion for two bitransitive Lie superalgebras to be
isomorphic 72
2. Various results on transitive Lie superalgebras 77
3. Construction of two types of transitive Lie superalgebras 83
4. Filtration of Lie superalgebras 86
§2 Some general properties of simple Lie superalgebras 91
1. Some elementary results on simple Lie superalgebras 91
2. Discussion of the 1-=- module Lt 96
3. Cartan subalgebras of a Lie superalgebra 108
§3 Lie superalgebras whose Killing form is non-degenerate 112
1. Some basic general results 112
2. The root space decomposition of a Lie superalgebra whose
Killing form is non-degenerate 120
§4 The classical simple Lie superalgebras 124
1. The general linear Lie superalgebra pi(V) 124
2. The special linear Lie superalgebra spl(V) 127
3. Subalgebras of pi(V) which leave invariant a homogeneous
non-degenerate bilinear form on V 129
A. The orthosymplectic Lie superalgebras 129
B. The Lie superalgebras b(n) 132
4. The (f,d) algebras of Gell-Mann, Michel, Radicati 133
5. Comments on the exceptional classical simple Lie super¬
algebras 134
6. The root space decomposition of the classical simple Lie
superalgebras 136
§5 Classification-of the classical simple Lie superalgebras 140
1. A trivial preliminary remark 142
2. L-t is not simple, ad1 is irreducible 143
3. L= is not simple, ad is not irreducible 148
4. Lq is simple I60
5. Extension of some classical simple Z - graded Lie super¬
algebras 163
§6 The Cartan Lie superalgebras 169
1. The Lie superalgebra W(V) of superderivations of an
exterior algebra 169
A. Definition and elementary properties of W(V) 169
B. W(V) as a sl(V) -module 173
C. W(V) as a universal transitive Z - graded Lie superalgebra 177
D. W(V) as a universal transitive filtered Lie superalgebra 181
2. The Lie superalgebras S(V) and S(V,t) 186
A. Elementary properties of S(V) 186
B. Elementary properties of S(V,t) , dimV even 189
C. Filtered Lie superalgebras whose associated Z - graded
Lie superalgebra is isomorphic to S(n) 191
3. The Lie superalgebras H(^) and H( p) 194
A. Elementary properties of H(i| ) and H(^) 194
B. A characterization of the algebras H(^) and H(i(;) 197
C. Filtered Lie superalgebras whose associated Z - graded
Lie superalgebra is isomorphic to H( ) or H(ijj) 202
§7 Classification of a special type of transitive Z - graded Lie
superalgebras 208
§8 The main classification theorems 222
Chapter III A survey of some further developments 231
§1 Superderivations of Clifford algebras and Lie superalgebras 231
1. Superderivations of a Clifford algebra 231
2. Superderivations of a Lie superalgebra 232
§2 A few remarks on nilpotent, solvable, and semi-simple Lie
superalgebras 236
1. Nilpotent and solvable Lie superalgebras 236
2. Semi-simple Lie superalgebras 237
§3 Finite-dimensional representations of simple Lie superalgebras 239
1. Lie superalgebras all of whose finite-dimensional represen¬
tations are completely reducible 239
2. Irreducible representations of simple Lie superalgebras 241
3. Generalized adjoint operations and star representations 243
Appendix 248
1. Notational conventions for reductive Lie algebras 248
2. Remarks on semi-simple Lie algebras and their representations 250
3. Special remarks on simple Lie algebras 252
4. A technical lemma 254
5. The index of a representation 258
References and foot-notes 262
Subject index 266
|
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| isbn | 3540092560 0387092560 |
| language | English |
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| physical | X, 271 S. |
| publishDate | 1979 |
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| publisher | Springer |
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| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Scheunert, Manfred Verfasser aut The theory of Lie superalgebras an introduction Manfred Scheunert Berlin [u.a.] Springer 1979 X, 271 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 716 Lie, Algèbres de Lie-algebra's gtt Superalgebra's gtt Lie superalgebras Lie-Algebra (DE-588)4130355-6 gnd rswk-swf Lie-Superalgebra (DE-588)4304027-5 gnd rswk-swf Lie-Superalgebra (DE-588)4304027-5 s DE-604 Lie-Algebra (DE-588)4130355-6 s Lecture notes in mathematics 716 (DE-604)BV000676446 716 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001483920&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Scheunert, Manfred The theory of Lie superalgebras an introduction Lecture notes in mathematics Lie, Algèbres de Lie-algebra's gtt Superalgebra's gtt Lie superalgebras Lie-Algebra (DE-588)4130355-6 gnd Lie-Superalgebra (DE-588)4304027-5 gnd |
| subject_GND | (DE-588)4130355-6 (DE-588)4304027-5 |
| title | The theory of Lie superalgebras an introduction |
| title_auth | The theory of Lie superalgebras an introduction |
| title_exact_search | The theory of Lie superalgebras an introduction |
| title_full | The theory of Lie superalgebras an introduction Manfred Scheunert |
| title_fullStr | The theory of Lie superalgebras an introduction Manfred Scheunert |
| title_full_unstemmed | The theory of Lie superalgebras an introduction Manfred Scheunert |
| title_short | The theory of Lie superalgebras |
| title_sort | the theory of lie superalgebras an introduction |
| title_sub | an introduction |
| topic | Lie, Algèbres de Lie-algebra's gtt Superalgebra's gtt Lie superalgebras Lie-Algebra (DE-588)4130355-6 gnd Lie-Superalgebra (DE-588)4304027-5 gnd |
| topic_facet | Lie, Algèbres de Lie-algebra's Superalgebra's Lie superalgebras Lie-Algebra Lie-Superalgebra |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001483920&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
| work_keys_str_mv | AT scheunertmanfred thetheoryofliesuperalgebrasanintroduction |