作者: 明確 時(shí)間: 2025-3-21 22:27
https://doi.org/10.1007/978-3-658-40724-7lgebra ., which satisfies the Maurer–Cartan equation: . The set of twisting morphisms Tw(.,.) is shown to be representable both in . and in .: . Then we investigate the twisting morphisms which give rise to quasi-isomorphisms under the aforementioned identifications. We call them ..作者: 高腳酒杯 時(shí)間: 2025-3-22 01:52 作者: Highbrow 時(shí)間: 2025-3-22 05:19 作者: 錫箔紙 時(shí)間: 2025-3-22 12:48
C. Czerkinsky,J.-B. Sun,J. Holmgren (co)operad, Koszul complex and Koszul resolution. This last one provides us with the minimal model of the operad ., thereby defining the notion of .-algebra up to homotopy. In the last section, we extend this method to inhomogeneous quadratic operads.作者: 笨拙處理 時(shí)間: 2025-3-22 14:03
Pod and Seed Camouflage in the Genus ,systems, PBW and Gr?bner bases, distributive laws (Diamond Lemma), or combinatorics (partition poset method). The notion of shuffle operad plays a key role in this respect. We also introduce the Manin products constructions for operads.作者: 諄諄教誨 時(shí)間: 2025-3-22 19:34 作者: 結(jié)合 時(shí)間: 2025-3-23 01:18 作者: Harrowing 時(shí)間: 2025-3-23 01:46
The Many Defensive Mechanisms of Plantsg associative algebras, why should one consider the category of dg coassociative coalgebras? The conceptual explanation is given by the Koszul duality theory for operads: the operad . is Koszul and its Koszul dual operad is itself. In order to generalize the notion of twisting morphism to dg .-algeb作者: lambaste 時(shí)間: 2025-3-23 06:38 作者: 幼兒 時(shí)間: 2025-3-23 12:48 作者: 圓錐 時(shí)間: 2025-3-23 15:48 作者: Pander 時(shí)間: 2025-3-23 18:43
Twisting Morphisms,lgebra ., which satisfies the Maurer–Cartan equation: . The set of twisting morphisms Tw(.,.) is shown to be representable both in . and in .: . Then we investigate the twisting morphisms which give rise to quasi-isomorphisms under the aforementioned identifications. We call them ..作者: 彩色 時(shí)間: 2025-3-23 23:29 作者: intrigue 時(shí)間: 2025-3-24 02:24 作者: conifer 時(shí)間: 2025-3-24 07:41 作者: Arctic 時(shí)間: 2025-3-24 13:04 作者: 盲信者 時(shí)間: 2025-3-24 16:36 作者: CON 時(shí)間: 2025-3-24 20:38
https://doi.org/10.1007/978-3-658-40724-7lgebra ., which satisfies the Maurer–Cartan equation: . The set of twisting morphisms Tw(.,.) is shown to be representable both in . and in .: . Then we investigate the twisting morphisms which give rise to quasi-isomorphisms under the aforementioned identifications. We call them ..作者: Clumsy 時(shí)間: 2025-3-25 00:28
C. Czerkinsky,J.-B. Sun,J. Holmgren (co)operad, Koszul complex and Koszul resolution. This last one provides us with the minimal model of the operad ., thereby defining the notion of .-algebra up to homotopy. In the last section, we extend this method to inhomogeneous quadratic operads.作者: Acquired 時(shí)間: 2025-3-25 03:19 作者: 外觀 時(shí)間: 2025-3-25 08:32
General Conclusions and Policy Implications, plays a role in many classification problems, like for instance deformation theory. We use the resolutions provided by the Koszul duality theory to make explicit small chain complexes which computes it.作者: Aspirin 時(shí)間: 2025-3-25 14:43 作者: 半導(dǎo)體 時(shí)間: 2025-3-25 17:26 作者: ascetic 時(shí)間: 2025-3-25 20:28
https://doi.org/10.1007/978-3-642-30362-318D50, 17AXX, 18G50, 55P48, 57T30; Koszul duality; higher algebra; homotopical algebra; operad; twisting 作者: 火海 時(shí)間: 2025-3-26 00:16 作者: Middle-Ear 時(shí)間: 2025-3-26 05:22
Jean-Pierre Kraehenbuhl,Marian R. NeutraThe aim of this chapter is to develop homological algebra in the operadic context.作者: antidote 時(shí)間: 2025-3-26 10:18 作者: hankering 時(shí)間: 2025-3-26 15:09
Book 2012ions. Higher operationsform new types of algebras. The key to understanding and comparing them, to creating invariants of their action is operad theory. This is a point of view that is 40 years old in algebraic topology, but the new trend is its appearance in several other areas, such as algebraic g作者: 小卒 時(shí)間: 2025-3-26 20:51 作者: Communal 時(shí)間: 2025-3-26 20:58 作者: 極端的正確性 時(shí)間: 2025-3-27 01:26
Koszul Duality for Associative Algebras,the preceding method to handle the inhomogeneous quadratic case. Two examples are: the universal enveloping algebra . of a Lie algebra . (original example due to J.-L. Koszul) and the Steenrod algebra.作者: deriver 時(shí)間: 2025-3-27 08:50
Bar and Cobar Construction of an Algebra over an Operad,otions of twisting morphism, bar and cobar constructions. When the operad . is Koszul, this allows us to define functorial quasi-free resolutions for .-algebras and .-algebras. They will be used in the next chapter to compute homology groups.作者: MAL 時(shí)間: 2025-3-27 12:52
Pod and Seed Camouflage in the Genus ,ture is homotopy equivalent to the starting data. The operadic framework with the Koszul duality theory enables us to state explicitly this transfer of structure result..In this chapter, we give four equivalent definitions for the notion of homotopy .-algebra. We also introduce the notion of ∞-morphisms.作者: 巨大沒(méi)有 時(shí)間: 2025-3-27 16:52
0072-7830 sumé.A new and conceptual presentation of the Koszul duality.In many areas of mathematics some “higher operations” are arising. These havebecome so important that several research projects refer to such expressions. Higher operationsform new types of algebras. The key to understanding and comparing 作者: gerontocracy 時(shí)間: 2025-3-27 20:28 作者: PHAG 時(shí)間: 2025-3-27 22:26
The Many Defensive Mechanisms of Plantsf operads. We prove that this operad is Koszul and we make explicit its Koszul dual and its Koszul resolution. In this way, we recover the notion of homotopy associative algebra introduced by Jim Stasheff. Finally, we give the . for this kind of algebras.作者: JADED 時(shí)間: 2025-3-28 04:07
Algebraic Operad,e . which is a unit. The existence of this structure follows readily from the universal properties of free algebras. Such a data . is called an ...This notion admits another equivalent definitions: classical, partial, and combinatorial.作者: Spinal-Fusion 時(shí)間: 2025-3-28 07:04
The Operads , and ,,,f operads. We prove that this operad is Koszul and we make explicit its Koszul dual and its Koszul resolution. In this way, we recover the notion of homotopy associative algebra introduced by Jim Stasheff. Finally, we give the . for this kind of algebras.作者: 記成螞蟻 時(shí)間: 2025-3-28 12:38
Homotopy Operadic Algebras,ture is homotopy equivalent to the starting data. The operadic framework with the Koszul duality theory enables us to state explicitly this transfer of structure result..In this chapter, we give four equivalent definitions for the notion of homotopy .-algebra. We also introduce the notion of ∞-morphisms.作者: 期滿 時(shí)間: 2025-3-28 16:36
Examples of Algebraic Operads,ry, harmonic analysis, algebraic combinatorics, theoretical physics, computer science. Of course, this list does not exhaust the examples appearing in the existing literature. The reader may have a look at the cornucopia of types of algebras . to find more examples.作者: boisterous 時(shí)間: 2025-3-28 20:08
0072-7830 a are given, for instance the Homotopy Transfer Theorem. Although the necessary notions of algebra are recalled, readers are expected to be familiar with elementary homological algebra. Each chapter ends with a978-3-642-44835-5978-3-642-30362-3Series ISSN 0072-7830 Series E-ISSN 2196-9701 作者: 散步 時(shí)間: 2025-3-28 23:23 作者: Fluctuate 時(shí)間: 2025-3-29 03:05 作者: Omniscient 時(shí)間: 2025-3-29 07:53
Algebras, Coalgebras, Homology, review the notions of associative, commutative and Lie algebra. Then we deal with the notion of coalgebra, which is going to play a key role in this book. This leads to the notion of convolution. The last sections cover bialgebras, pre-Lie algebras, differential graded objects and convolution algeb作者: hypnogram 時(shí)間: 2025-3-29 14:34
Twisting Morphisms,lgebra ., which satisfies the Maurer–Cartan equation: . The set of twisting morphisms Tw(.,.) is shown to be representable both in . and in .: . Then we investigate the twisting morphisms which give rise to quasi-isomorphisms under the aforementioned identifications. We call them ..作者: Emmenagogue 時(shí)間: 2025-3-29 18:56
Koszul Duality for Associative Algebras,find a method to construct this minimal model when . is quadratic, that is .=.(.)/(.) where the ideal (.) is generated by .?... We will see that the quadratic data (.,.) permits us to construct explicitly a coalgebra . and a twisting morphism .. Then, applying the theory of Koszul morphisms given in作者: Pelvic-Floor 時(shí)間: 2025-3-29 22:00
Algebraic Operad,gory . of vector spaces to itself, . is equipped with a monoid structure, that is a transformation of functors ., which is associative, and another one . which is a unit. The existence of this structure follows readily from the universal properties of free algebras. Such a data . is called an ...Thi作者: Ancillary 時(shí)間: 2025-3-30 02:18
Koszul Duality of Operads, (co)operad, Koszul complex and Koszul resolution. This last one provides us with the minimal model of the operad ., thereby defining the notion of .-algebra up to homotopy. In the last section, we extend this method to inhomogeneous quadratic operads.
