This is the first extensive treatment of the theory of corings and their comodules. In the first
part, the module-theoretic aspects of coalgebras over commutative rings are described …

Doi-Koppinen Hopf modules and entwined modules unify various kinds of modules that
have been intensively studied over the past decades, such as Hopf modules, graded …

Given a ring A and an A-coring C, we study when the forgetful functor from the category of
right C-comodules to the category of right A-modules and its right adjoint−⊗ AC are …

For a given entwining structure (A, C) ψinvolving an algebraA, a coalgebraC, and an
entwining map ψ: C⊗ A→ A⊗ C, a categoryMCA (ψ) of right (A, C) ψ-modules is defined and …

We reformulate the concept of connection on a Hopf–Galois extension B⊆ P in order to
apply it in computing the Chern–Connes pairing between the cyclic cohomology HC 2 n (B) …

The deformation complex of an algebra over a colored PROP P is defined in terms of a
minimal (or, more generally, cofibrant) model of P. It is shown that it carries the structure of …

The key part of the definition of a Hopf-Galois extension B⊂ A over the Hopf algebra H is
bijectivity of a canonical map β: A⊗ BA→ A⊗ H. We develop criteria under which surjectivity …

We construct a quantum version of the SU (2) Hopf bundle S 7→ S 4. The quantum sphere S
7 q arises from the symplectic group Sp q (2) and a quantum 4-sphere S 4 q is obtained via …

We study the corings whose category of right comodules has a finitely generated projective
generator. In order to extricate the structure of these corings, we introduce the notion of …

We develop the noncommutative geometry (bundles, connections etc.) associated to
algebras that factorise into two subalgebras. An example is the factorisation of matrices M 2 …