Quantum Groups and Noncommutative Geometry
Members of the Research Group
- Ludwik Dabrowski
- Cesare Reina
- Francesco D'Andrea
- Lucio Cirio
Main External Collaborators
- Giovanni Landi
(Trieste)
- Andrzej Sitarz (Krakow, Poland)
- Joseph C. Varilly (San Jose', Costa Rica)
Main Research lines
- Non-commutative geometry and quantum field theory.
- Dirac operators on quantum homogeneous spaces and construction of spectral triples.
- ADHM construction of non-commutative instatons in SUq(2) gauge theories. Non commutative
moduli spaces.
- Representations of SUq(2) at roots of unity and extensions of the spin covering with
applications to exotic statistics.
Research plans
The research plans for next few years concentrate on two main lines.
- The construction of instantons and their moduli spaces on quantum spaces, and their
applications. A first task is to complete the study of quantum
moduli spaces for instantons on quantum S4. In the longer perspective this serves
to valuate the possibility to set up the stage for a generic quantum 4-manifold,
in view of non-commutative generalizations of the Donaldson theorem.
- The study of the differential structure (Riemannian metric and spin) on quantum spaces,
and their applications. Firstly, we intend to proceed with the study of the relations between
the quantum group deformations and the Connes spectral triples.