Related papers: Cyclic duality between BV algebras and BV modules
We study the biclosedness of the monoidal categories of modules and comodules over a (left or right) Hopf algebroid, along with the bimodule category centres of the respective opposite categories and a corresponding categorical equivalence…
The Hochschild and (cotriple) cyclic homologies of crossed modules of (not-necessarily-unital) associative algebras are investigated. Wodzicki's excision theorem is extended for inclusion crossed modules in the category of crossed modules…
In this note, we outline the general development of a theory of symmetric homology of algebras, an analog of cyclic homology where the cyclic groups are replaced by symmetric groups. This theory is developed using the framework of crossed…
Binary operations on algebras of observables are studied in the quantum as well as in the classical case. It is shown that certain natural compatibility conditions with the associative product imply the properties which usually are…
We provide an analog of the Drinfeld quantum double construction in the context of crossed Hopf group coalgebras introduced by Turaev. We prove that, provided the base group is finite, the double of a semisimple crossed Hopf group coalgebra…
We construct a Hopf action, with an invariant trace, of a bicrossed product Hopf algebra $\cH=\big( \cU(\Fg_1) \acr \cR(G_2) \big)^{\cop}$ constructed from a matched pair of Lie groups $G_1$ and $G_2$, on a convolution algebra…
Curved algebras are a generalization of differential graded algebras which have found numerous applications recently. The goal of this foundational article is to introduce the notion of a curved operad, and to develop the operadic calculus…
We prove that the algebra $\cal{A}$ of chord diagrams, the dual to the associated graded algebra of Vassiliev knot invariants, is isomorphic to the universal enveloping algebra of a Casimir Lie algebra in a certain tensor category (the PROP…
Two cochain complexes are constructed for an algebra A and a coalgebra C entwined with each other via the map $\psi:C\otimes A\to A\otimes C$. One complex is associated to an A-bimodule, the other to a C-bicomodule. In the former case the…
We describe a new small cyclic operad model QBV for the dg dual operad of the Batalin-Vilkovisky operad. As an application, we show that the Feynman transform of BV is quasi-isomorphic to the amputated Feynman transform of the dg dual, in…
The notion of vertex operator coalgebra is presented and motivated via the geometry of conformal field theory. Specifically, we describe the category of geometric vertex operator coalgebras, whose objects have comultiplicative structures…
Let H be a coFrobenius Hopf algebra over a field k. Let A be a right H-comodule algebra over k. We recall that the category of right H-comodules admits a certain model structure whose homotopy category is equivalent to the stable category…
This article introduces a method, which starting from simple and quite general mathematical data, allows to construct linear algebras of operators which are, each of them, endowed with a bialgebra structure (coproduct and counity). Moreover…
In this paper we study the cyclic cohomology of certain x-Hopf algebras: universal enveloping algebras, quantum algebraic tori, the Connes-Moscovici x-Hopf algebroids and the Kadison bialgebroids. Introducing their stable anti…
We define two coproducts for cycle-free oriented graphs, thus building up two commutative con- nected graded Hopf algebras, such that one is a comodule-coalgebra on the other, thus generalizing the result obtained previously for Hopf…
We show that the family of standard simplices and the family of Stasheff polytopes are dual to each other in the following sense. The chain modules of the standard simplices, resp. the Stasheff polytopes, assemble to give an operad. We show…
Using general principles in the theory of vertex operator algebras and their twisted modules, we obtain a bosonic, twisted construction of a certain central extension of a Lie algebra of differential operators on the circle, for an…
We study the operad of associative algebras equipped with a derivation. We show that it is determined by polynomials in several variables and substitution. Replacing polynomials by rational functions gives an operad which is isomorphic to…
In this paper, we compute the cyclic homology of the Taft algebras and of their Auslander algebras. Given a Hopf algebra $\Lambda,$ the Grothendieck groups of projective $\Lambda -$modules and of all $\Lambda -$modules are endowed with a…
We study the hairy graph homology of a cyclic operad; in particular we show how to assemble corresponding hairy graph cohomology classes to form cocycles for ordinary graph homology, as defined by Kontsevich. We identify the part of hairy…