We construct a noncommutative deformation of odd-dimensional spheres that preserves the natural partition of the (2N + 1)-dimensional sphere into (N + 1)many solid tori. This generalizes the case N = 1 referred to as the Heegaard quantum sphere. Our twisted odd-dimensional quantum sphere C∗-algebras are given as multipullback C∗-algebras. We prove that they are isomorphic to the universal C∗-al...

Manin associated to a quadratic algebra (quantum space) the quantum matrix group of its automorphisms. This Talk aims to demonstrate that Manin’s construction can be extended for quantum spaces which are nonquadratic homogeneous algebras. Here given a regular Artin-Schelter algebra of dimension 3 we construct the quantum group of its symmetries, i.e., the Hopf algebra of its automorphisms. For ...

It is shown that quantum homogeneous spaces of a quantum group H can be viewed as fibres of quantum fibrations with the total space H that are dual to coalgebra bundles. As concrete examples of such structures the fibrations with the quantum 2-sphere and the quantum hyperboloid fibres are considered.