We construct noncommutative principal fibrations S θ 7→ S θ 4 which are deformations of
the classical SU (2) Hopf fibration over the four sphere. We realize the noncommutative …

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 …

To any cleft Hopf Galois object, ie, any algebra Hα obtained from a Hopf algebra H by
twisting its multiplication with a two-cocycle α, we attach two “universal algebras” AHα and …

arXiv:math/0212264v1 [math.QA] 19 Dec 2002 Page 1 arXiv:math/0212264v1 [math.QA] 19
Dec 2002 THE GARDEN OF QUANTUM SPHERES LUDWIK DA BROWSKI Scuola …

We explore several aspects of algebraic noncommutative spaces described explicitly. In
particular, we examine the construction of noncommutative Euclidean spaces by Dubois …

Symmetries play a central role in both physics and mathematics. In physics, they can be
found at the heart of practically any theory where they encode an invariance of the theory …

In the 1990's, results coming from diverse areas of mathematics and mathematical physics
pointed in the direction of a new notion of symmetry which subsumes both quantum …

Of particular interest for both mathematics and physics are non-abelian gauge theories
introduced by CN Yang and R. Mills in 1954 [53]. They are generalization of Maxwell's …

In this paper, we review some recent developments of compact quantum groups that arise
as θ-deformations of compact Lie groups of rank at least two. A θ-deformation is merely a 2 …

We prove a criterion of when a coaction of a compact Lie group on an algebra of continuous
functions on a compact manifold extends to a coaction of deformation quantizations of the …