We construct quantum group-valued canonical connections on quantum homogeneous spaces, including a q-deformed Dirac monopole on the quantum sphere of Podles quantum differential coming from the 3-Dâ€¦ (More)

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 âˆ’ âŠ—A C are separable. We thenâ€¦ (More)

We introduce a large class of bicovariant differential calculi on any quantum group A, associated to Ad-invariant elements. For example, the deformed trace element on SLq(2) recovers Woronowiczâ€™ 4DÂ±â€¦ (More)

For a given entwining structure involving an algebra A, a coalgebra C, and an entwining map Ïˆ : CâŠ—Aâ†’ AâŠ—C, a category of right (A,C,Ïˆ)-modules is defined and its structure analysed. It is shown thatâ€¦ (More)

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 âˆ’ âŠ—A C are separable. We thenâ€¦ (More)

Abstract. To any bimodule that is finitely generated and projective on one side one can associate a coring, known as a comatrix coring. A new description of comatrix corings in terms of dataâ€¦ (More)

We develop a generalised gauge theory in which the role of gauge group is played by a coalgebra and the role of principal bundle by an algebra. The theory provides a unifying point of view whichâ€¦ (More)

We develop the noncommutative geometry (bundles, connections etc.) associated to algebras that factorise into two subalgebras. An example is the factorisation of matrices M2(C) = CZ2 Â· CZ2. We alsoâ€¦ (More)

We show that certain embeddable homogeneous spaces of a quantum group that do not correspond to a quantum subgroup still have the structure of quantum quotient spaces. We propose a construction ofâ€¦ (More)

Non-commutative connections of the second type or hom-connections and associated integral forms are studied as generalisations of right connections of Manin. First, it is proven that the existence ofâ€¦ (More)