This is a mini-review about generalized instantons of noncommutative gauge theories in
dimensions 4, 6 and 8, with emphasis on their realizations in type II string theory, their …

The C*-algebras of continuous functions on quantum spheres, quantum real projective
spaces, and quantum complex projective spaces are realized as Cuntz-Krieger algebras …

We study the quantum sphere as a quantum Riemannian manifold in the quantum frame
bundle approach. We exhibit its 2-dimensional cotangent bundle as a direct sum Ω 0, 1⊕ Ω …

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 …

Quantum Symmetry Groups of Noncommutative Spheres Page 1 Commun. Math. Phys. 221,
511 – 523 (2001) Communications in Mathematical Physics © Springer-Verlag 2001 Quantum …

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

We develop the description of non-commutative geometry of the 4-dimensional quantum
Hall fluid's theory proposed recently by Zhang and Hu. The non-commutative structure of …

We describe noncommutative geometric aspects of twisted deformations, in particular of the
spheres of Connes and Landi and of Connes and Dubois Violette, by using the differential …

We give an introductory survey to the use of Hopf algebras in several problems of
noncommutative geometry. The main example, the Hopf algebra of rooted trees, is a graded …

Galois comodules of a coring are studied. The conditions for a simple comodule to be a
Galois comodule are found. A special class of Galois comodules termed principal …