7 papers
Chern numbers for two families of noncommutative Hopf fibrations
Piotr M. Hajac, Rainer Matthes, Wojciech Szymanski
We consider noncommutative line bundles associated with the Hopf fibrations of SUq(2) over all Podles spheres and with a locally trivial Hopf fibration of S^3_{pq}. These bundles a…
A locally trivial quantum Hopf bundle
R. Matthes
We describe a locally trivial quantum principal U(1)-bundle over the quantum space S^2_{pq} which is a noncommutative analogue of the usual Hopf bundle. We also provide results con…
Quantum Real Projective Space, Disc and Sphere
Piotr M. Hajac, Rainer Matthes, Wojciech Szymanski
We define the -algebra of quantum real projective space , classify its irreducible representations and compute its -theory. We also show that the -disc of Klim…
Gauge transformations on locally trivial quantum principal fibre bundles
Dirk Calow, Rainer Matthes
If P, B, H are the algebras of the total space, the base space, and the structure group of a locally trivial principal fibre bundle (QPFB), left (right) gauge transformations are d…
Locally trivial quantum vector bundles and associated vector bundles
Dirk Calow, Rainer Matthes
We define locally trivial quantum vector bundles (QVB) and QVB associated to locally trivial quantum principal fibre bundles. There exists a differential structure on the associate…
Connes' trace formula and Dirac realization of Maxwell and Yang-Mills action
P. M. Alberti, R. Matthes
The paper covers known facts about the Dixmier trace (with some generalities about traces), the Wodzicki residue, and Connes' trace theorem, including two variants of proof of the…