Free Lie algebras:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford
Clarendon Press
1993
|
| Series: | London Mathematical Society: [London Mathematical Society monographs / New series]
7 Oxford science publications |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | XVII, 269 S. graph. Darst. |
| ISBN: | 0198536798 9780198536796 |
Staff View
MARC
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| 245 | 1 | 0 | |a Free Lie algebras |c Christophe Reutenauer |
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Record in the Search Index
| _version_ | 1804122592548749312 |
|---|---|
| adam_text | Contents
Index of notation xv
0. Introduction 1
0.1 The Poincare Birkhoff Witt theorem 1
0.2 Free Lie algebras 4
0.3 Elimination 7
0.4 Appendix 12
0.5 Notes 13
1. Lie polynomials 14
1.1 Words, polynomials, and series 14
1.2 Lie polynomials 18
1.3 Characterizations of Lie polynomials 19
1.4 Shuffles 23
1.5 Duality concatenation/shuffle 26
1.6 Appendix 33
1.7 Notes 39
2. Algebraic properties 40
2.1 The weak algorithm 40
2.2 Subalgebras 44
2.3 Automorphisms 45
2.4 Free sets of Lie polynomials 49
2.5 Appendix 50
2.6 Notes 51
3. Logarithms and exponentials 52
3.1 Lie series and logarithm 52
3.2 The canonical projections 57
3.3 Coefficients of the Hausdorff series 61
3.4 Derivation and exponentiation 76
3.5 Appendix 80
3.6 Notes 82
xii Contents
4. Hall bases 84
4.1 Hall trees and words 84
4.2 Hall and Poincare Birkhoff Witt bases 89
4.3 Hall sets and Lazard sets 98
4.4 Appendix 101
4.5 Notes 103
5. Applications of Hall sets 105
5.1 Lyndon words and basis 105
5.2 The dual basis 108
5.3 The derived series 112
5.4 Order properties of Hall sets 114
5.5 Synchronous codes 119
5.6 Appendix 124
5.7 Notes 126
6. Shuffle algebra and sub words 127
6.1 The free generating set of Lyndon words 127
6.2 Presentation of the shuffle algebra 129
6.3 Subword functions 131
6.4 The lower central series of the free group 136
6.5 Appendix 147
6.6 Notes 152
7. Circular words 154
7.1 The number of primitive necklaces 154
7.2 Hall words and primitive necklaces 158
7.3 Generation of Lyndon words 161
7.4 Factorization into Lyndon words 163
7.5 Words and multisets of primitive necklaces 166
7.6 Appendix 170
7.7 Notes 174
8. The action of the symmetric group 176
8.1 Action of the symmetric group and of the linear group 176
8.2 The character of the free Lie algebra 180
8.3 Irreducible components 185
8.4 Lie idempotents 194
8.5 Representations on the canonical decomposition 201
8.6 Appendix 206
8.7 Notes 215
Contents xiii
9. The Solomon descent algebra 217
9.1 The descent algebra 217
9.2 Idempotents 224
9.3 Homomorphisms 233
9.4 Quasisymmetric functions and enumeration of permutations 242
9.5 Appendix 248
9.6 Notes 254
References 256
Index 267
|
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| discipline | Mathematik |
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| id | DE-604.BV008207242 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:16:20Z |
| institution | BVB |
| isbn | 0198536798 9780198536796 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-005416379 |
| oclc_num | 246854471 |
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| physical | XVII, 269 S. graph. Darst. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | Clarendon Press |
| record_format | marc |
| series2 | London Mathematical Society: [London Mathematical Society monographs / New series] Oxford science publications |
| spelling | Reutenauer, Christophe 1953- Verfasser (DE-588)129256277 aut Free Lie algebras Christophe Reutenauer Oxford Clarendon Press 1993 XVII, 269 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier London Mathematical Society: [London Mathematical Society monographs / New series] 7 Oxford science publications Hier auch später erschienene, unveränderte Nachdrucke Lie-Algebra (DE-588)4130355-6 gnd rswk-swf Freie Lie-Algebra (DE-588)4326747-6 gnd rswk-swf Freie Lie-Algebra (DE-588)4326747-6 s DE-604 Lie-Algebra (DE-588)4130355-6 s New series] London Mathematical Society: [London Mathematical Society monographs 7 (DE-604)BV045355493 7 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005416379&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Reutenauer, Christophe 1953- Free Lie algebras Lie-Algebra (DE-588)4130355-6 gnd Freie Lie-Algebra (DE-588)4326747-6 gnd |
| subject_GND | (DE-588)4130355-6 (DE-588)4326747-6 |
| title | Free Lie algebras |
| title_auth | Free Lie algebras |
| title_exact_search | Free Lie algebras |
| title_full | Free Lie algebras Christophe Reutenauer |
| title_fullStr | Free Lie algebras Christophe Reutenauer |
| title_full_unstemmed | Free Lie algebras Christophe Reutenauer |
| title_short | Free Lie algebras |
| title_sort | free lie algebras |
| topic | Lie-Algebra (DE-588)4130355-6 gnd Freie Lie-Algebra (DE-588)4326747-6 gnd |
| topic_facet | Lie-Algebra Freie Lie-Algebra |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005416379&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV045355493 |
| work_keys_str_mv | AT reutenauerchristophe freeliealgebras |