Algebraic operads / Jean-Louis Loday, Bruno Vallette.
Series Grundlehren der mathematischen wissenschaften ; v. 346Editor: New York : Springer, 2012Descripción: 634 p. : il. ; 23 cmISBN: 9783642448355; 978364230362-3 (eBook)Otra clasificación: 18D50 (16E99)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 Résumé [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 lor Inhomogeneous Quadratic Algebras [75] -- 3.7 Résumé [82] -- 3.8 Exercises [85] -- 4 Methods to Prove Koszulity of an Algebra [89] -- 4.1 Rewriting Method [90] -- 4.2 Reduction by Filtration -- 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 Résumé [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 ol the Comparison Lemma [51] -- 2.6 Résumé [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 ol 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 lor Inhomogeneous Quadratic Algebras [75] -- 3.7 Résumé [82] -- 3.8 Exercises [85] -- 4 Methods to Prove Koszulity of an Algebra [89] -- 4.1 Rewriting Method [90] -- 4.2 Reduction by Filtration -- 4.3 Poincaré-Birkhoff-Witt Bases and Gröbner Bases [99] -- 4.4 Koszul Duality Theory and Lattices [109] -- 4.5 Manin Products for Quadratic Algebras [111] -- 4.6 Résumé [114] -- 4.7 Exercises [116] -- 5 Algebraic Operad [119] -- 5.1 S-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 of an Operad [159] -- 5.7 Type of Algebras [162] -- 5.8 Cooperad [166] -- 5.9 Nonsymmetric Operad [175] -- 5.10 Résumé [186] -- 5.11 Exercises [188] -- 6 Operadic Homological Algebra [193] -- 6.1 Infinitesimal Composite [194] -- 6.2 Differential Graded S-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 of the Operadic Comparison Lemmas [222] -- 6.8 Résumé [225] -- 6.9 Exercises [227] -- 7 Koszul Duality of Operads [229] -- 7.1 Operadic Quadratic Data, Quadratic Operad and Coopered [230] -- 7.2 Koszul Dual (Co)Operad of 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 Résumé [258] -- 7.10 Exercises [260] -- 8 Methods to Prove Koszulity of 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] -- 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 Résumé [317] -- 8.10 Exercises [320] -- 9 The Operads As and Aqq [325] -- 9.1 Associative Algebras and the Operad Ass [326] -- 9.2 Associative Algebras Up to Homotopy [336] -- 9.3 The Bar-Cobar Construction on As [343] -- 9.4 Homotopy Transfer Theorem for the Operad As [345] -- 9.5 An Example of an Aoo-Algebra with Nonvanishing my [353] -- 9.6 Résumé [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 Résumé [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 Algebras [408] -- 11.3 Bar-Cobar Adjunction for Algebras [413] -- 11.4 Homotopy Theory of Algebras [417] -- 11.5 Résumé [424] -- 11.6 Exercises [426] -- 12 (Co)Homology of Algebras over an Operad [427] -- 12.1 Homology of Algebras over an Operad [428] -- 12.2 Deformation Theory of Algebra Structures [433] -- 12.3 André-Quillcn (Co)HomoIogy of Algebras over an Operad [447] -- 12.4 Operadic Cohomology of Algebras with Coefficients [464] -- 12.5 Résurmé [470] -- 12.6 Exercises [473] -- 13 Examples of 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] -- 13.6 Dendriform Algebras and Diassociative Algebras [522] -- 13.7 Batalin-Vilkovisky Algebras and the Operad BV [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 of Operads with 1-Ary Operations, 0-Ary Operation [550] -- 13.13 Generalized Bialgebras and Triples of 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 Sn [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. 1 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] --
| Item type | Home library | Shelving location | Call number | Materials specified | Status | Date due | Barcode |
|---|---|---|---|---|---|---|---|
Libros
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Instituto de Matemática, CONICET-UNS | Últimas adquisiciones | 18 L821 (Browse shelf) | Available | A-9425 |
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 Résumé [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 lor Inhomogeneous Quadratic Algebras [75] --
3.7 Résumé [82] --
3.8 Exercises [85] --
4 Methods to Prove Koszulity of an Algebra [89] --
4.1 Rewriting Method [90] --
4.2 Reduction by Filtration --
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 Résumé [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 ol the Comparison Lemma [51] --
2.6 Résumé [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 ol 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 lor Inhomogeneous Quadratic Algebras [75] --
3.7 Résumé [82] --
3.8 Exercises [85] --
4 Methods to Prove Koszulity of an Algebra [89] --
4.1 Rewriting Method [90] --
4.2 Reduction by Filtration --
4.3 Poincaré-Birkhoff-Witt Bases and Gröbner Bases [99] --
4.4 Koszul Duality Theory and Lattices [109] --
4.5 Manin Products for Quadratic Algebras [111] --
4.6 Résumé [114] --
4.7 Exercises [116] --
5 Algebraic Operad [119] --
5.1 S-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 of an Operad [159] --
5.7 Type of Algebras [162] --
5.8 Cooperad [166] --
5.9 Nonsymmetric Operad [175] --
5.10 Résumé [186] --
5.11 Exercises [188] --
6 Operadic Homological Algebra [193] --
6.1 Infinitesimal Composite [194] --
6.2 Differential Graded S-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 of the Operadic Comparison Lemmas [222] --
6.8 Résumé [225] --
6.9 Exercises [227] --
7 Koszul Duality of Operads [229] --
7.1 Operadic Quadratic Data, Quadratic Operad and Coopered [230] --
7.2 Koszul Dual (Co)Operad of 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 Résumé [258] --
7.10 Exercises [260] --
8 Methods to Prove Koszulity of 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] --
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 Résumé [317] --
8.10 Exercises [320] --
9 The Operads As and Aqq [325] --
9.1 Associative Algebras and the Operad Ass [326] --
9.2 Associative Algebras Up to Homotopy [336] --
9.3 The Bar-Cobar Construction on As [343] --
9.4 Homotopy Transfer Theorem for the Operad As [345] --
9.5 An Example of an Aoo-Algebra with Nonvanishing my [353] --
9.6 Résumé [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 Résumé [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 Algebras [408] --
11.3 Bar-Cobar Adjunction for Algebras [413] --
11.4 Homotopy Theory of Algebras [417] --
11.5 Résumé [424] --
11.6 Exercises [426] --
12 (Co)Homology of Algebras over an Operad [427] --
12.1 Homology of Algebras over an Operad [428] --
12.2 Deformation Theory of Algebra Structures [433] --
12.3 André-Quillcn (Co)HomoIogy of Algebras over an Operad [447] --
12.4 Operadic Cohomology of Algebras with Coefficients [464] --
12.5 Résurmé [470] --
12.6 Exercises [473] --
13 Examples of 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] --
13.6 Dendriform Algebras and Diassociative Algebras [522] --
13.7 Batalin-Vilkovisky Algebras and the Operad BV [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 of Operads with 1-Ary Operations, 0-Ary Operation [550] --
13.13 Generalized Bialgebras and Triples of 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 Sn [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. 1 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] --
MR, REVIEW #
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