4 citations · 16 across the 16 of their papers we have counts for
23 papers
Duality for action bialgebroids
Sophie Chemla, Fabio Gavarini, Niels Kowalzig
We study the effect of linear duality on action bialgebroids (also known as smash product or scalar extension bialgebroids) and, for those bearing a quantisation nature, the effect…
Hopf bimodules for bialgebroids
Sophie Chemla, Niels Kowalzig
Generalising a result for Hopf algebras, we not only define the four possible types of Hopf modules in the bialgebroid setting but also yield the notion of two-sided two-cosided Ho…
Takeuchi-Schneider equivalence and calculi for homogeneous spaces of Hopf algebroids
Niels Kowalzig, Thomas Weber
We develop a notion of covariant differential calculus for Hopf algebroids. As a byproduct, we prove analogues of the fundamental theorem of Hopf modules and a Takeuchi-Schneider e…
Higher structures on homology groups
Niels Kowalzig, Francesca Pratali
We dualise the classical fact that an operad with multiplication leads to cohomology groups which form a Gerstenhaber algebra to the context of cooperads: as a result, a cooperad w…
Cyclic duality between BV algebras and BV modules
Niels Kowalzig
We show that if an operad is at the same time a cosimplicial object such that the respective structure maps are compatible with the operadic composition in a natural way, then one…
Universal enveloping algebras of Lie-Rinehart algebras: crossed products, connections, and curvature
Xavier Bekaert, Niels Kowalzig, Paolo Saracco
We extend a theorem, originally formulated by Blattner-Cohen-Montgomery for crossed products arising from Hopf algebras weakly acting on noncommutative algebras, to the realm of le…
Brackets and products from centres in extension categories
Domenico Fiorenza, Niels Kowalzig
Building on Retakh's approach to Ext groups through categories of extensions, Schwede reobtained the well-known Gerstenhaber algebra structure on Ext groups over bimodules of assoc…
Centres, trace functors, and cyclic cohomology
Niels Kowalzig
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 oppo…
A noncommutative calculus on the cyclic dual of Ext
Niels Kowalzig
We show that if the cochain complex computing Ext groups (in the category of modules over Hopf algebroids) admits a cocyclic structure, then the noncommutative Cartan calculus stru…
Cyclic Gerstenhaber-Schack cohomology
Domenico Fiorenza, Niels Kowalzig
We show that the diagonal complex computing the Gerstenhaber-Schack cohomology of a bialgebra (that is, the cohomology theory governing bialgebra deformations) can be given the str…
Higher brackets on cyclic and negative cyclic (co)homology
Domenico Fiorenza, Niels Kowalzig
The purpose of this article is to embed the string topology bracket developed by Chas-Sullivan and Menichi on negative cyclic cohomology groups as well as the dual bracket found by…
When Ext is a Batalin-Vilkovisky algebra
Niels Kowalzig
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…
Cyclic homology arising from adjunctions
Niels Kowalzig, Ulrich Kraehmer, Paul Slevin
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 Y…
Morita theory for Hopf algebroids, principal bibundles, and weak equivalences
Laiachi El Kaoutit, Niels Kowalzig
We show that two flat commutative Hopf algebroids are Morita equivalent if and only if they are weakly equivalent and if and only if there exists a principal bibundle connecting th…
Duality features of left Hopf algebroids
Sophie Chemla, Fabio Gavarini, Niels Kowalzig
We explore special features of the pair (U^*, U_*) formed by the right and left dual over a (left) bialgebroid U in case the bialgebroid is, in particular, a left Hopf algebroid. I…
Gerstenhaber and Batalin-Vilkovisky structures on modules over operads
Niels Kowalzig
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 th…
Batalin-Vilkovisky algebra structures on (Co)Tor and Poisson bialgebroids
Niels Kowalzig
In this article, we extend our preceding studies on higher algebraic structures of (co)homology theories defined by a left bialgebroid (U,A). For a braided commutative Yetter-Drinf…
Batalin-Vilkovisky Structures on Ext and Tor
Niels Kowalzig, Ulrich Kraehmer
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,…
Morita base change in Hopf-cyclic (co)homology
Laiachi El Kaoutit, Niels Kowalzig
In this paper, we establish the invariance of cyclic (co)homology of left Hopf algebroids under the change of Morita equivalent base algebras. The classical result on Morita invari…
Cyclic structures in algebraic (co)homology theories
Niels Kowalzig, Ulrich Kraehmer
This note discusses the cyclic cohomology of a left Hopf algebroid (-Hopf algebra) with coefficients in a right module-left comodule, defined using a straightforward gene…
The cyclic theory of Hopf algebroids
Niels Kowalzig, Hessel Posthuma
We give a systematic description of the cyclic cohomology theory of Hopf algebroids in terms of its associated category of modules. Then we introduce a dual cyclic homology theory…
Duality and products in algebraic (co)homology theories
Niels Kowalzig, Ulrich Kraehmer
The origin and interplay of products and dualities in algebraic (co)homology theories is ascribed to a -Hopf algebra structure on the relevant universal enveloping algebr…
Phase Space Reduction of Star Products on Cotangent Bundles
Niels Kowalzig, Nikolai Neumaier, Markus J. Pflaum
In this paper we construct star products on Marsden-Weinstein reduced spaces in case both the original phase space and the reduced phase space are (symplectomorphic to) cotangent b…