Combinatorial aspects of Lie superalgebras:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton [u.a.]
CRC Press
1995
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VIII, 260 S. 1 Diskette (3,5") |
| ISBN: | 0849389607 |
Internformat
MARC
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| 100 | 1 | |a Michalev, Aleksandr A. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Combinatorial aspects of Lie superalgebras |c Alexander A. Mikhalev ; Andrej A. Zolotykh |
| 264 | 1 | |a Boca Raton [u.a.] |b CRC Press |c 1995 | |
| 300 | |a VIII, 260 S. |e 1 Diskette (3,5") | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
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| 689 | 0 | 1 | |a Kombinatorik |0 (DE-588)4031824-2 |D s |
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| 700 | 1 | |a Zolotych, Andrej A. |e Verfasser |4 aut | |
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| 940 | 1 | |n oe | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-007086326 | ||
Datensatz im Suchindex
| _version_ | 1804125097105031168 |
|---|---|
| adam_text | Contents
Introduction v
1 Preliminaries 1
1 Lie superalgebras 1
Algebras 1
Lie algebras 3
G graded algebras 4
Lie superalgebras 5
2 Color Lie superalgebras 7
Commutation factor 7
Color tensor product 10
Free e commutative associative algebra 10
Color Lie superalgebras 12
Skew envelope of a color Lie superalgebra 19
Differential Lie superalgebras 20
3 Universal constructions 21
Free associative algebras 21
The free color Lie superalgebra 23
Universal enveloping algebras 24
Free products 26
4 Group actions on free Lie superalgebras 27
5n modules and GL(F) modules 27
Lie idempotents 29
Klyachko s theorem 31
Characters and multiplicities of representations .... 33
Comments 36
2 Linear Structure 39
5 Regular words 39
New letters 40
Elementary properties 41
Cyclic conjugates 43
i
ii CONTENTS
Factorization 45
Ambiguities 46
6 Regular monomials 47
7 Arrangements of brackets 49
8 Bases of free color Lie superalgebras 51
Lyndon Shirshov bases 52
Other bases 54
Bases of the free color Lie p superalgebra 56
PBW basis of the free associative algebra 58
Witt formulas 58
Identical relations among left normed monomials ... 62
Images of inner derivations 63
9 Dynkin Specht Wever criterion 65
10 Equations in free Lie superalgebras 67
11 Algorithms and examples 69
Algorithms 69
Examples 72
Comments 73
3 Free Subalgebras 75
12 Weak algorithm 76
13 Reduced subsets 78
Subsets Z(x) and W(z) 78
Subsets ZP{x) and W(z) 80
Reduced subsets 81
14 Main theorem 82
Nielsen property 82
Schreier property 84
Generators of the automorphism group 88
15 Finitely generated subalgebras 89
Reduced finite subsets 89
Schreier formulas 90
Intersection of subalgebras of finite rank 91
The odd component of a subalgebra of finite rank ... 93
16 Subalgebras of infinite rank 94
The even components 94
Fixed points of finite groups of linear automorphisms . 96
17 Algorithms and examples 97
Algorithms 98
Examples 100
Comments 101
CONTENTS iii
4 Canonical Bases 103
18 Canonical bases in associative algebras 103
Diamond Lemma 104
Triangle rule 106
Grobner bases of left ideals 107
Examples of canonical bases in associative algebras . . 108
19 Universal enveloping algebras 113
PBW theorems for Lie superalgebras 113
Separability 115
PBW theorems for differential Lie superalgebras .... 118
Remarks 120
Universal enveloping algebras as graded Hopf algebras 122
BCH problem for Lie superalgebras 126
Free shuffle superalgebras 129
20 Canonical bases in Lie superalgebras 131
Compositions 131
Composition Lemma 135
Applications of Composition Lemma 141
21 Free products 143
Bases of free products 144
Subalgebras of free products 147
22 Algorithms and examples 149
Algorithms 149
Examples 152
Comments 155
5 Free Differential Calculus 157
23 Universal derivations 158
Free differential calculus 158
Elementary properties of derivatives 163
24 Jacobian matrices 164
Jacobians 164
Jacobian conjecture for free Lie superalgebras 165
25 Admissible elements 168
Main auxiliary lemma 168
Admissible sets 171
26 The homogeneous case 175
27 Rank theorems 182
Rank of an element 182
Rank of a system of elements 187
28 Automorphisms and primitive elements 189
Criteria of primitivity 189
Cohomological dimension 1 192
Images of primitive elements 195
iv CONTENTS
29 Algorithms and examples 203
Algorithms 203
Examples 207
Comments 215
Appendix Program Description 217
How the program works 217
The meaning of the keys 218
The main field (ring) of coefficients 219
The type of the free algebra 219
Operands and operators 219
CALS and TfiX 221
Examples of CALS applications 221
Bibliography 225
Notations 255
Index 257
|
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| author | Michalev, Aleksandr A. Zolotych, Andrej A. |
| author_facet | Michalev, Aleksandr A. Zolotych, Andrej A. |
| author_role | aut aut |
| author_sort | Michalev, Aleksandr A. |
| author_variant | a a m aa aam a a z aa aaz |
| building | Verbundindex |
| bvnumber | BV010624338 |
| classification_rvk | SK 340 |
| ctrlnum | (OCoLC)260188321 (DE-599)BVBBV010624338 |
| discipline | Mathematik |
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| id | DE-604.BV010624338 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:56:08Z |
| institution | BVB |
| isbn | 0849389607 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007086326 |
| oclc_num | 260188321 |
| open_access_boolean | |
| owner | DE-12 DE-19 DE-BY-UBM DE-739 |
| owner_facet | DE-12 DE-19 DE-BY-UBM DE-739 |
| physical | VIII, 260 S. 1 Diskette (3,5") |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | CRC Press |
| record_format | marc |
| spelling | Michalev, Aleksandr A. Verfasser aut Combinatorial aspects of Lie superalgebras Alexander A. Mikhalev ; Andrej A. Zolotykh Boca Raton [u.a.] CRC Press 1995 VIII, 260 S. 1 Diskette (3,5") txt rdacontent n rdamedia nc rdacarrier Superalgebra (DE-588)4304028-7 gnd rswk-swf Kombinatorik (DE-588)4031824-2 gnd rswk-swf Superalgebra (DE-588)4304028-7 s Kombinatorik (DE-588)4031824-2 s DE-604 Zolotych, Andrej A. Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007086326&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Michalev, Aleksandr A. Zolotych, Andrej A. Combinatorial aspects of Lie superalgebras Superalgebra (DE-588)4304028-7 gnd Kombinatorik (DE-588)4031824-2 gnd |
| subject_GND | (DE-588)4304028-7 (DE-588)4031824-2 |
| title | Combinatorial aspects of Lie superalgebras |
| title_auth | Combinatorial aspects of Lie superalgebras |
| title_exact_search | Combinatorial aspects of Lie superalgebras |
| title_full | Combinatorial aspects of Lie superalgebras Alexander A. Mikhalev ; Andrej A. Zolotykh |
| title_fullStr | Combinatorial aspects of Lie superalgebras Alexander A. Mikhalev ; Andrej A. Zolotykh |
| title_full_unstemmed | Combinatorial aspects of Lie superalgebras Alexander A. Mikhalev ; Andrej A. Zolotykh |
| title_short | Combinatorial aspects of Lie superalgebras |
| title_sort | combinatorial aspects of lie superalgebras |
| topic | Superalgebra (DE-588)4304028-7 gnd Kombinatorik (DE-588)4031824-2 gnd |
| topic_facet | Superalgebra Kombinatorik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007086326&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT michalevaleksandra combinatorialaspectsofliesuperalgebras AT zolotychandreja combinatorialaspectsofliesuperalgebras |