5 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 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…