# The Cobar Construction As A Hopf Algebra

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### BATALIN-VILKOVISKY ALGEBRAS AND CYCLIC

by LUC MENICHI Cited by 64 Gerstenhaber algebra, is to remark as in [7] that the Cobar construction on. H, ΩH, is orem 1.6 and Connes-Moscovici cyclic cohomology of Hopf algebras [17].

### On some applications of the cobar construction

cobar construction, so that H(X)=HF(C#(X)) as Hopf algebras, strengthening the original result of Adams. The homotopies involved may be used to define

### A computational approach of A ∞-(co)algebras - Taylor

1⊗n−i. The following connected commutative dg-Hopf algebras with null differential are important in our applications. the degree in the cobar construction;.

### Cyclic cohomology and Hopf algebra symmetry - Inspire HEP

by H Moscovici Cited by 2 construction of the modular square. Keywords: noncommutative geometry, cyclic cohomology, Hopf algebras, quantum groups. Mathematics Subject

### Homotopy theory of monoids and derived localization - City

recent generalization of Adams's cobar-construction to the non-simply connected case, and a new algebraic model for the homotopy theory of connected topological spaces By construction it is a morphism of Hopf algebras, compat- ible with

### K

by T BAUER 2014 Cited by 5 Eilenberg-Moore spectral sequence, Morava K-theory, cobar construction, spectral sequence commutative and cocommutative Hopf algebra as well, with.

### Decomposition spaces in Combinatorics

by I Gálvez-Carrillo 2016 Cited by 24 Hopf algebra, the Fa`a di Bruno bialgebra, the Butcher Connes Kreimer Hopf algebra The same construction works for elements in a monoid (with the finite decomposition The cobar construction as a Hopf algebra.

### Extension Theory for Connected Hopf Algebras

by WM Singer 1972 Cited by 93 Similarly, the acyclic cobar construction. I' (K) acquires a B-action. We describe these structures in Section 4. These observations suggest the definition of the

### Brace Bar-Cobar Duality

by J Young 2013 Cited by 7 that the classical cobar construction from coalgebras to algebras Ω : CoAlg →. Alg can be enhanced to a functor from Hopf algebras to E2

### ON A MULTIPLICATIVITY UP TO HOMOTOPY OF THE - EMIS

by Z KHAREBAVA 2002 Cited by 1 with product µE introduced by Baues in [3], [4] are Hopf algebras. In this paper we shall Thus the Cobar construction of a DGC is a DGA with 1 : R → R as unit.

### The homotopy theory of coalgebras over a comonad

by K HESS 2013 Cited by 33 in descent theory and in the theory of Hopf-Galois extensions. These examples A in terms of a generalized cobar construction. Contents. 1. familiar to practitioners of rational and algebraic homotopy theory. As long as the.

### THE LOOP GROUP AND THE COBAR CONSTRUCTION

by K HESS 2010 Cited by 22 is naturally a primitively generated Hopf algebra, and the chain alge In degree zero the cobar construction is a free associative algebra on

### Rectifications of A∞-algebras 1 1 Introduction - Universidad

by MJ Jiménez Cited by 11 not a Hopf algebra). Every morphism of Given a simply connected DG coalgebra C, the reduced cobar construction, ¯Ω(C), is a. DG algebra whose

### BP - MIMUW

by ML ADAMASZEK 2010 We assume the reader is familiar with the general theory of Hopf algebroids and their homological algebra and with the construction of the Adams-Novikov

### The cobar construction as a Hopf algebra

by HJ Baues 1998 Cited by 61 Abstract. We show that the integral cobar construction Xg├И of a 1-reduced simplicial set И has the structure of a homotopy Hopf algebra. This leads to.

### The double bar and cobar constructions - Numdam

by HJ Baues 1981 Cited by 72 of Pontryagin - algebras. f2 C*X is the cobar construction on the coalgebra map and let hN : SN ~ PN ~ PR,N be the Hopf map, that is the attach- ing map of the

### Homotopy BV-algebra structure on the double cobar

by A Quesney 2016 Cited by 3 The cobar construction oH of an involutive Hopf algebra turns out to be the underlying complex in the Hopf-cyclic Hochschild cohomology of H,

### ON THE COHOMOLOGY OF SOME HOPF ALGEBRAS

by A Iwai 1967 Cited by 30 To calculate Extb (K9K) for an algebra B, it is sometimes convenient to use an injective resolution for the coalgebra B* (for example, cobar construction).

### THE COBAR CONSTRUCTION AS AN E∞-HOPF ALGEBRA

THE COBAR CONSTRUCTION AS AN E∞-HOPF ALGEBRA. ANIBAL M. MEDINA-MARDONES AND YOUR NAME. Abstract. Contents. 1. Introduction. 1. 2.

### Connected Hopf algebras of dimension p2p2

29 Jun 2013 Let H be a finite-dimensional connected Hopf algebra over an as the homology of the cobar construction of K In Proposition 6.2, we.

### Chromatic unstable homotopy, plethories, and the Dieudonné

18 Aug 2016 A∗ dual Steenrod algebra, a commutative Fp-Hopf algebra. H∗X, H∗Y It forces us to use the cobar construction unsuitable for daily use!

### Research by Volodymyr V. Lyubashenko Research Field

For an abelian braided tensor category we investigate a Hopf algebra F in it, the braided We provide bar and cobar constructions as functors between some

### The Cohomology Algebras of Finite Dimensional Hopf Algebras

by C Wilkerson 1981 Cited by 52 Cohomology of Hopf algebras, Steenrod operations, Steenrod algebra, spectral cobar construction on A*, Adams [1]: B*(A*) is the free tensor algebra on the.

### THE HOCHSCHILD HOMOLOGY OF A(1). Contents 1

by A SALCH 2015 Cited by 1 homology of a finite-dimensional Hopf algebra R might be linearly dual to the A → A ⊗k A. By the cyclic cobar construction on A we mean the cosimplicial k-

### Abstract - NC State Repository

by Z Kharebava 2004 be a Hopf algebra up to homotopy, then weak equivalence classes of such Thus the Cobar construction of a 1-connected DGC is a connected DGA with.

### A localization theorem in homological algebra

by HR MILLER Cited by 28 homology of the cobar construction 0.(8; -). For a description of Let G be a DG Hopf algebra with commutative multiplication and let Sbea supplemented DG

### To the left of the sphere spectrum1 §1. Bivariant theories

Adams/bar/cobar construction) followed by a weak equivalence. This is an defines a coaction of the elementary Hopf algebra E(β), so we can describe the.

### Full-Text PDF

by N Shimada 1986 Cited by 3 It is characterizing that A is a quotient of the reduced cobar construction. C(A*) ([!] there appeared similar constructions of resolutions over (Hopf) algebras [15],.

### Batalin-Vilkovisky Algebras, Operads, and Hopf Algebroids

Brace Bar-Cobar Duality, E2 cochains, and BV algebras 630 of A by A. In the first part of the talk, we recall the details of this construction.

### An of the - J-Stage

by N Shimada 1986 Cited by 3 It is characterizing that A is a quotient of the reduced cobar construction. C(A*) ([!]), where A* means the dual Hopf algebra [12] of the mod p Steenrod algebra A

### The functor of singular chains detects weak homotopy

by M Rivera 2018 Cited by 7 The cobar construction of the χ-coalgebra of normalized singular chains has a further property: the 0th homology of its cobar construc- tion is a Hopf algebra, i.e.

### PROGRAMA FONDECYT INFORME FINAL ETAPA 2009

shuffle bialgebra, in such a way that the Hopf algebra structures defined on the cobar construction for permutades gives differential objects, which coincide

### ON THE COHOMOLOGY OF SOME HOPF ALGEBRAS

by N Shimada 1967 Cited by 30 To calculate Extb (K9K) for an algebra B, it is sometimes convenient to use an injective resolution for the coalgebra B* (for example, cobar construction).

### Three Hopf algebras from number theory, physics & topology

by I Gálvez Carrillo Cited by 4 eral variations of the construction of the Connes Kreimer Hopf algebra based for example on planar labeled trees, labeled trees, unlabeled trees and trees

### ON THE COBAR CONSTRUCTION OF A BIALGEBRA 1

by T KADEISHVILI 2005 Cited by 31 which form on the cobar construction ΩC of a DG-bialgebra, a structure of (reduced) cobar construction ΩC on C is a DG-algebra whose underlying graded [1] J. Adams, On the non-existence of elements of Hopf invariant one, Ann. Math.

### What is loop multiplication anyhow? - University of Rochester

by JA Neisendorfer Cited by 2 the Hopf algebra structure of the loop space. Contents. 1. Introduction. 2. 2. The cobar construction on a differential graded coalgebra. 4. 3. Cotensor products

### The Cohomology of Restricted Lie Algebras and of Hopf

by JP MAY Cited by 158 In theory, the bar construction suflices to calculate the homology groups of an augmented algebra. In practice, the bar construction is generally too large (has too

### Hopf Algebroids and Their Cyclic Theory

by N KOWALZIG 2009 Cited by 31 More applications of Hopf algebras comprise e.g. the construction of invariants in topology and knot theory [OKoLeRoTu, Tu], and appear in

### COCHAIN OPERATIONS DEFINING STEENROD i - EuDML

by T Kadeishvili 2003 Cited by 19 DG hyphen Hopf algebra period This diagonal allows one to produce the next cobar construction Capital Omega Capital Omega C sub * open parenthesis

### Hopf measuring comonoids and enrichment - Department of

by M Hyland 2017 Cited by 16 The classical construction of the Sweedler dual A. ◦ of a k-algebra [29] satisfies two important properties: A. ◦ is a bialgebra if A is so, and A.

### The deformation complex for differential graded Hopf algebras

by RN Umble 1996 Cited by 16 Abstract. Let H be a differential graded Hopf algebra (d.g.h.a.) over a field k. This paper gives an explicit construction of a triple cochain complex that defines the

### Koszul Duality for En Algebras

by Y Fu 2018 3.1 Bar Construction for Associative Algebras Observe that the coBar functor lands in this subcategory: write O! = colimk O!,≤k, where O! To upgrade to an equivalence of cocommutative Hopf algebras one has to loop our.

### Scissors congruences and the bar and cobar constructions

by JL Cathelineau 2003 Cited by 5 A Hopf algebra of spherical polytopes introduced more than 20 years ago by C.H. Sah, in his book on scissors congruences, is revisited through the light of shu

### THE LOOP GROUP AND THE COBAR CONSTRUCTION

by K Hess 2010 Cited by 22 is naturally a primitively generated Hopf algebra, and the chain algebra In degree zero the cobar construction is a free associative algebra on

### Hopf Algebras and Actions, Part II Seattle Workshop 2016

17 Apr 2016 veloping algebras. This construction recovers almost all of the known connected Hopf algebras of finite GK-dimension, and leads to many.

### COCHAIN OPERATIONS DEFINING STEENROD i - EMIS

by T KADEISHVILI 2003 Cited by 19 which turns the cobar construction into a DG-Hopf algebra. This diagonal allows one to produce the next cobar construction ΩΩC∗(X) which models the.

### An algebraic model for the loop space homology of a

by K Hess 2007 Cited by 16 the homotopy fiber of a morphism of chain Hopf algebras. make extended use of one-sided cobar constructions, which we apply in innovative.

### A Computational approach of A∞-(co)algebras

by A Berciano-Alcaraz Cited by 6 the reduced cobar construction of C is the dg-algebra Ω(A) = Ts−1 ( ¯C) with CHCM=chain complex; A=dg-algebra; C=dg-coalgebra; HA=dg-Hopf algebra.

### Homotopy BV-algebra structure on the double cobar

by A Quesney Cited by 3 The cobar construction oH of an involutive Hopf algebra turns out to be the underly- ing complex in the Connes-Moscovici cyclic coHochschild

### Localization at b10 in the stable category of comodules over

by EK Belmont 2018 Cited by 3 associated to an extension of Hopf algebras B. A. C. We present a similar construction that can be defined if B is only an A-comodule algebra, instead of a Hopf.