Algebraic operads:
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Heidelberg ; New York ; Dordrecht ; London
Springer
[2012]
|
| Schriftenreihe: | Grundlehren der mathematischen Wissenschaften
346 |
| Schlagwörter: | |
| Links: | http://deposit.dnb.de/cgi-bin/dokserv?id=4017472&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025157197&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | xxiv, 634 Seiten Illustrationen |
| ISBN: | 9783642303616 |
| ISSN: | 0072-7830 |
Internformat
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Datensatz im Suchindex
| _version_ | 1819270527856934912 |
|---|---|
| adam_text | IMAGE 1
CONTENTS
1 ALGEBRAS, COALGEBRAS, HOMOLOGY 1
1.1 CLASSICAL ALGEBRAS (ASSOCIATIVE, COMMUTATIVE, LIE) 1
1.2 COASSOCIATIVE COALGEBRAS 9
1.3 BIALGEBRA 14
1.4 PRE-LIE ALGEBRAS 20
1.5 DIFFERENTIAL GRADED ALGEBRA 22
1.6 CONVOLUTION 32
1.7 RESUME 34
1.8 EXERCISES 34
2 TWISTING MORPHISMS 37
2.1 TWISTING MORPHISMS 38
2.2 BAR AND COBAR CONSTRUCTION 41
2.3 KOSZUL MORPHISMS 48
2.4 COBAR CONSTRUCTION AND QUASI-ISOMORPHISMS 49
2.5 PROOF OF THE COMPARISON LEMMA 51
2.6 RESUME 55
2.7 EXERCISES 57
3 KOSZUL DUALITY FOR ASSOCIATIVE ALGEBRAS 61
3.1 QUADRATIC DATA, QUADRATIC ALGEBRA, QUADRATIC COALGEBRA 62
3.2 KOSZUL DUAL OF A QUADRATIC ALGEBRA 64
3.3 . BAR AND COBAR CONSTRUCTION ON A QUADRATIC DATA 66
3.4 KOSZUL ALGEBRAS 69
3.5 GENERATING SERIES 73
3.6 KOSZUL DUALITY THEORY FOR INHOMOGENEOUS QUADRATIC ALGEBRAS . 75 3.7
RESUME 82
3.8 EXERCISES 85
4 METHODS TO PROVE KOSZULITY O F AN ALGEBRA 89
4.1 REWRITING METHOD 9 0
4.2 REDUCTION BY FILTRATION 92
X I
HTTP://D-NB.INFO/1021740675
IMAGE 2
XII C O N T E N T S
4.3 POINCARE-BIRKHOFF-WITT BASES AND GROBNER BASES 99
4.4 KOSZUL DUALITY THEORY AND LATTICES 109
4.5 MANIN PRODUCTS FOR QUADRATIC ALGEBRAS I L L
4.6 RESUME 114
4.7 EXERCISES 116
5 ALGEBRAIC OPERAD 119
5.1 §-MODULE AND SCHUR FUNCTOR 121
5.2 ALGEBRAIC OPERAD AND ALGEBRA OVER AN OPERAD 130
5.3 CLASSICAL AND PARTIAL DEFINITION OF AN OPERAD 142
5.4 VARIOUS CONSTRUCTIONS ASSOCIATED TO AN OPERAD 149
5.5 FREE OPERAD 154
5.6 COMBINATORIAL DEFINITION O F AN OPERAD 159
5.7 TYPE OF ALGEBRAS 162
5.8 COOPERAD 166
5.9 NONSYMMETRIC OPERAD 175
5.10 RESUME 186
5.11 EXERCISES 188
6 OPERADIC HOMOLOGICAL ALGEBRA 193
6.1 INFINITESIMAL COMPOSITE 194
6.2 DIFFERENTIAL GRADED §-MODULE 197
6.3 DIFFERENTIAL GRADED OPERAD 199
6.4 OPERADIC TWISTING MORPHISM 208
6.5 OPERADIC BAR AND COBAR CONSTRUCTION 214
6.6 OPERADIC KOSZUL MORPHISMS 220
6.7 PROOF O F THE OPERADIC COMPARISON LEMMAS 222
6.8 RESUME 225
6.9 EXERCISES 227
7 KOSZUL DUALITY O F OPERADS 229
7.1 OPERADIC QUADRATIC DATA, QUADRATIC OPERAD AND COOPERAD . . . . 230
7.2 KOSZUL DUAL (CO)OPERAD O F A QUADRATIC OPERAD 233
7.3 BAR AND COBAR CONSTRUCTION ON AN OPERADIC QUADRATIC DATA . . . 236
7.4 KOSZUL OPERADS 237
7.5 GENERATING SERIES 241
7.6 BINARY QUADRATIC OPERADS 243
7.7 NONSYMMETRIC BINARY QUADRATIC OPERAD 250
7.8 KOSZUL DUALITY FOR INHOMOGENEOUS QUADRATIC OPERADS 252
7.9 RESUME 258
7.10 EXERCISES 260
8 METHODS TO PROVE KOSZULITY O F AN OPERAD 263
8.1 REWRITING METHOD FOR BINARY QUADRATIC NS OPERADS 264
8.2 SHUFFLE OPERAD 266
8.3 REWRITING METHOD FOR OPERADS 274
8.4 REDUCTION BY FILTRATION 277
IMAGE 3
C O N T E N T S XIII
8.5 PBW BASES AND GROBNER BASES FOR OPERADS 283
8.6 DISTRIBUTIVE LAWS 288
8.7 PARTITION POSET METHOD 297
8.8 MANIN PRODUCTS 308
8.9 RESUME 317
8.10 EXERCISES 320
9 THE OPERADS A S AND AOO 325
9.1 ASSOCIATIVE ALGEBRAS AND THE OPERAD .4^5 326
9.2 ASSOCIATIVE ALGEBRAS UP TO HOMOTOPY 336
9.3 THE BAR-COBAR CONSTRUCTION ON A S 343
9.4 HOMOTOPY TRANSFER THEOREM FOR THE OPERAD /U 345
9.5 AN EXAMPLE OF AN ACO-ALGEBRA WITH NONVANISHING M3 353
9.6 RESUME 355
9.7 EXERCISES 356
10 HOMOTOPY OPERADIC ALGEBRAS 359
10.1 HOMOTOPY ALGEBRAS: DEFINITIONS 360
10.2 HOMOTOPY ALGEBRAS: MORPHISMS 369
10.3 HOMOTOPY TRANSFER THEOREM 376
10.4 INVERSE OF OO-ISOMORPHISMS AND OO-QUASI-ISOMORPHISMS 386 10.5
HOMOTOPY OPERADS 391
10.6 RESUME 399
10.7 EXERCISES 401
11 BAR AND COBAR CONSTRUCTION OF AN ALGEBRA OVER AN OPERAD 405
11.1 TWISTING MORPHISM FOR ALGEBRAS 406
11.2 BAR AND COBAR CONSTRUCTION FOR ^ - A L G E B R A S 408
11.3 BAR-COBAR ADJUNCTION FOR ^ - A L G E B R A S 413
11.4 HOMOTOPY THEORY O F ALGEBRAS 417
11.5 RESUME 424
11.6 EXERCISES 426
12 (CO)HOMOLOGY O F ALGEBRAS OVER AN OPERAD 427
12.1 HOMOLOGY OF ALGEBRAS OVER AN OPERAD 428
12.2 DEFORMATION THEORY OF ALGEBRA STRUCTURES 433
12.3 ANDRE-QUILLEN (CO)HOMOLOGY O F ALGEBRAS OVER AN OPERAD . . . . 447
12.4 OPERADIC COHOMOLOGY OF ALGEBRAS WITH COEFFICIENTS 464
12.5 RESUME 470
12.6 EXERCISES 473
13 EXAMPLES O F ALGEBRAIC OPERADS 479
13.1 COMMUTATIVE ALGEBRAS AND THE OPERAD COM 480
13.2 LIE ALGEBRAS AND THE OPERAD LIE 490
13.3 POISSON ALGEBRAS, GERSTENHABER ALGEBRAS AND THEIR OPERAD . . . 502
13.4 PRE-LIE ALGEBRAS AND PERM-ALGEBRAS 514
13.5 LEIBNIZ ALGEBRAS AND ZINBIEL ALGEBRAS 519
IMAGE 4
X I V C O N T E N T S
13.6 DENDRIFORM ALGEBRAS AND DIASSOCIATIVE ALGEBRAS 522
13.7 BATALIN-VILKOVISKY ALGEBRAS AND THE OPERAD B V 531
13.8 MAGMATIC ALGEBRAS 539
13.9 PARAMETRIZED BINARY QUADRATIC OPERADS 541
13.10 JORDAN ALGEBRAS, INTERCHANGE ALGEBRAS 542
13.11 MULTI-ARY ALGEBRAS 544
13.12 EXAMPLES O F OPERADS WITH 1-ARY OPERATIONS, 0-ARY OPERATION . .
550 13.13 GENERALIZED BIALGEBRAS AND TRIPLES O F OPERADS 553
13.14 TYPES OF OPERADS 559
APPENDIX A THE SYMMETRIC GROUP 567
A. 1 ACTION OF GROUPS 567
A.2 REPRESENTATIONS OF THE SYMMETRIC GROUP § 569
APPENDIX B CATEGORIES 573
B.L CATEGORIES AND FUNCTORS 573
B.2 ADJOINT FUNCTORS, FREE OBJECTS 577
B.3 MONOIDAL CATEGORY 580
B.4 MONADS 583
B.5 CATEGORIES OVER FINITE SETS 585
B.6 MODEL CATEGORIES 587
B.7 DERIVED FUNCTORS AND HOMOLOGY THEORIES 592
APPENDIX C TREES 597
C.L PLANAR BINARY TREES 597
C.2 PLANAR TREES AND STASHEFF POLYTOPE 600
C.3 TREES AND REDUCED TREES 603
C.4 GRAPHS 605
REFERENCES 609
INDEX 625
LIST OF NOTATIONS 633
|
| any_adam_object | 1 |
| author | Loday, Jean-Louis 1946-2012 Vallette, Bruno |
| author_GND | (DE-588)122970756 (DE-588)1028282362 |
| author_facet | Loday, Jean-Louis 1946-2012 Vallette, Bruno |
| author_role | aut aut |
| author_sort | Loday, Jean-Louis 1946-2012 |
| author_variant | j l l jll b v bv |
| building | Verbundindex |
| bvnumber | BV040302184 |
| classification_rvk | SK 200 SK 320 |
| ctrlnum | (OCoLC)802609324 (DE-599)DNB1021740675 |
| dewey-full | 512.02 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.02 |
| dewey-search | 512.02 |
| dewey-sort | 3512.02 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV040302184 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T16:12:00Z |
| institution | BVB |
| isbn | 9783642303616 |
| issn | 0072-7830 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025157197 |
| oclc_num | 802609324 |
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| owner_facet | DE-384 DE-824 DE-20 DE-83 DE-19 DE-BY-UBM DE-188 DE-11 |
| physical | xxiv, 634 Seiten Illustrationen |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | Springer |
| record_format | marc |
| series | Grundlehren der mathematischen Wissenschaften |
| series2 | Grundlehren der mathematischen Wissenschaften |
| spellingShingle | Loday, Jean-Louis 1946-2012 Vallette, Bruno Algebraic operads Grundlehren der mathematischen Wissenschaften Operade (DE-588)4638722-5 gnd Kategorientheorie (DE-588)4120552-2 gnd |
| subject_GND | (DE-588)4638722-5 (DE-588)4120552-2 |
| title | Algebraic operads |
| title_auth | Algebraic operads |
| title_exact_search | Algebraic operads |
| title_full | Algebraic operads Jean-Louis Loday, Bruno Vallette |
| title_fullStr | Algebraic operads Jean-Louis Loday, Bruno Vallette |
| title_full_unstemmed | Algebraic operads Jean-Louis Loday, Bruno Vallette |
| title_short | Algebraic operads |
| title_sort | algebraic operads |
| topic | Operade (DE-588)4638722-5 gnd Kategorientheorie (DE-588)4120552-2 gnd |
| topic_facet | Operade Kategorientheorie |
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| volume_link | (DE-604)BV000000395 |
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