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Algebraic operads:

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Bibliographic Details
Main Authors:	Loday, Jean-Louis 1946-2012 (Author), Vallette, Bruno (Author)
Format:	Book
Language:	English
Published:	Heidelberg ; New York ; Dordrecht ; London Springer [2012]
Series:	Grundlehren der mathematischen Wissenschaften 346
Subjects:	Kategorientheorie Operade
Online Access:	Inhaltstext Inhaltsverzeichnis
Physical Description:	xxiv, 634 Seiten Illustrationen
ISBN:	9783642303616
ISSN:	0072-7830

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MARC


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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
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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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spelling	Loday, Jean-Louis 1946-2012 Verfasser (DE-588)122970756 aut Algebraic operads Jean-Louis Loday, Bruno Vallette Heidelberg ; New York ; Dordrecht ; London Springer [2012] © 2012 xxiv, 634 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Grundlehren der mathematischen Wissenschaften 346 0072-7830 Kategorientheorie (DE-588)4120552-2 gnd rswk-swf Operade (DE-588)4638722-5 gnd rswk-swf Kategorientheorie (DE-588)4120552-2 s Operade (DE-588)4638722-5 s 1\p DE-604 Vallette, Bruno Verfasser (DE-588)1028282362 aut Erscheint auch als Online-Ausgabe 978-3-642-30362-3 Grundlehren der mathematischen Wissenschaften 346 (DE-604)BV000000395 346 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=4017472&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf 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 Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk
spellingShingle	Loday, Jean-Louis 1946-2012 Vallette, Bruno Algebraic operads Grundlehren der mathematischen Wissenschaften Kategorientheorie (DE-588)4120552-2 gnd Operade (DE-588)4638722-5 gnd
subject_GND	(DE-588)4120552-2 (DE-588)4638722-5
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	Kategorientheorie (DE-588)4120552-2 gnd Operade (DE-588)4638722-5 gnd
topic_facet	Kategorientheorie Operade
url	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
volume_link	(DE-604)BV000000395
work_keys_str_mv	AT lodayjeanlouis algebraicoperads AT vallettebruno algebraicoperads

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