Let F be a field, Γ a finite group, and Map (Γ, F) the Hopf algebra of all set-theoretic maps Γ→
F. If E is a finite field extension of F and Γ is its Galois group, the extension is Galois if and …

We propose a sheaf-theoretic approach to the theory of differential calculi on quantum
principal bundles over non-affine bases. After recalling the affine case we define differential …

The purpose of this paper is to propose a sheaf theoretic approach to the theory of quantum
principal bundles over non affine bases. We study noncommutative principal bundles …

Abstract Algebras of functions on quantum weighted projective spaces are introduced, and
the structure of quantum weighted projective lines or quantum teardrops is described in …

The theory of general Galois-type extensions is presented, including the interrelations
between coalgebra extensions and algebra (co) extensions, properties of corresponding …

In this paper we develop the theory of reduction of quantum principal bundles over
projective bases. We show how the sheaf theoretic approach can be effectively applied to …

Let F be a field, G a finite group, and Map (G, F) the Hopf algebra of all set-theoretic maps G-
> F. If E is a finite field extension of F and G is its Galois group, the extension is Galois if and …

We introduce the notion of a locally trivial GC⁎-algebra, which is a noncommutative
counterpart of the total space of a locally compact Hausdorff numerable principal G-bundle …

Within the framework of free actions of compact quantum groups on unital C*-algebras, we
propose two conjectures. The first one states that, if $ H $ is the C*-algebra of a compact …

Two hierarchies of quantum principal bundles over quantum real projective spaces are
constructed. One hierarchy contains bundles with U (1) as a structure group, the other has …