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The cyclic theory of Hopf algebroids
We give a systematic description of the cyclic cohomology theory of Hopf alge\-broids in terms of its associated category of modules. Then we introduce a dual cyclic homology theory by applyingExpand
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Batalin-Vilkovisky Structures on Ext and Tor
This article studies the algebraic structure of homology theories defined by a left Hopf algebroid U over a possibly noncommutative base algebra A, such as for example Hochschild, Lie algebroid (inExpand
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When Ext is a Batalin-Vilkovisky algebra
We show under what conditions the complex computing general Ext-groups carries the structure of a cyclic operad such that Ext becomes a Batalin-Vilkovisky algebra. This is achieved by transferringExpand
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Duality and products in algebraic (co)homology theories
Abstract The origin and interplay of products and dualities in algebraic (co)homology theories is ascribed to a × A -Hopf algebra structure on the relevant universal enveloping algebra. This providesExpand
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Hopf Algebroids and Their Cyclic Theory
The main objective of this thesis is to clarify concepts of generalised symmetries in noncommutative geometry (i.e., the noncommutative analogue of groupoids and Lie algebroids) and their associatedExpand
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Gerstenhaber and Batalin–Vilkovisky Structures on Modules over Operads
In this article, we show under what additional ingredients a comp (or opposite) module over an operad with multiplication can be given the structure of a cyclic k-module and how the underlyingExpand
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Quantization, noncommutative geometry, and symmetry
Centres, trace functors, and cyclic cohomology
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 andExpand
CYCLIC HOMOLOGY ARISING FROM ADJUNCTIONS
Given a monad and a comonad, one obtains a distributive law between them from lifts of one through an adjunction for the other. In particular, this yields for any bialgebroid the Yetter-Drinfel'dExpand
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Cyclic structures in algebraic (co)homology theories
This note discusses the cyclic cohomology of a left Hopf algebroid ($\times_A$-Hopf algebra) with coefficients in a right module-left comodule, defined using a straightforward generalisation of theExpand
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