Seminars on Operator Algebras - Rome La Sapienza, Italy

Mercoledì 31 Ottobre 2007
Dipartimento di Matematica, Univ. Roma "Tor Vergata", Aula 1201

15:00 - 16:00 Prof. Lars Tuset, University of Oslo - QUANTUM GROUPS AS NON-COMMUTATIVE MANIFOLDS

Abstract: For the q-deformation of a compact simple Lie group we construct a biequivariant spectral triple, which is an isospectral deformation of that defined by the Dirac operator D on G. Our quantum Dirac operator D_q is a unitary twist of D considered as an element of the non-abelian Weyl algebra. We also produce regular spectral triples on all quantum homogenous spaces.
To show that the commutator of D_q with a regular function on the quantum group is bounded, we invoke the Drinfeld associator Φ_KZ which is given as the monodromy of the KZ-equations from conformal field theory. This requires that Φ_KZ is the coboundary of a unitary twist, which we show is the case in the analytic setting thanks to a deep result by Kazhdan and Lusztig on the equivalence of two monoidal categories.

16:30 - 17:30 Dr. Mihály Weiner, Alfréd Rényi Institute of Mathematics, Budapest - QUANTUM INFORMATION THEORY AND PAIRWISE QUASI-ORTHOGONAL SUBALGEBRAS

15:00 - 16:00	Prof. Lars Tuset, University of Oslo - QUANTUM GROUPS AS NON-COMMUTATIVE MANIFOLDS
15:00 - 16:00	Abstract: For the q-deformation of a compact simple Lie group we construct a biequivariant spectral triple, which is an isospectral deformation of that defined by the Dirac operator D on G. Our quantum Dirac operator D_q is a unitary twist of D considered as an element of the non-abelian Weyl algebra. We also produce regular spectral triples on all quantum homogenous spaces. To show that the commutator of D_q with a regular function on the quantum group is bounded, we invoke the Drinfeld associator Φ_KZ which is given as the monodromy of the KZ-equations from conformal field theory. This requires that Φ_KZ is the coboundary of a unitary twist, which we show is the case in the analytic setting thanks to a deep result by Kazhdan and Lusztig on the equivalence of two monoidal categories.
16:30 - 17:30	Dr. Mihály Weiner, Alfréd Rényi Institute of Mathematics, Budapest - QUANTUM INFORMATION THEORY AND PAIRWISE QUASI-ORTHOGONAL SUBALGEBRAS