Announcements
LECTURES
18 February 2013, 10:15-12:00
DEFORMATION QUANTIZATION OF HAMILTONIAN ACTIONS IN POISSON GEOMETRY
We recall the notion of a momentum map in Poisson geometry and describe the so-called Poisson reduction. The latter is a technique that allows one to reduce the dimension of a manifold in the presence of symmetries implemented by Poisson actions. Using the tools of deformation quantization and quantum groups, we define a quantum momentum map in such a way that it generates quantum actions.
CHIARA ESPOSITO (Universitat Autonoma de Barcelona)
18 February 2013, 14:15-16:00
C*-ALGEBRAS GENERATED BY q-NORMAL OPERATORS
S. L. Woronowicz's theory of generating C*-algebras by unbounded operators is applied to q-normal operators satisfying the defining relation of the quantum complex plane. A non-unital C*-algebra generated in this sense can be interpreted as the algebra of continuous functions vanishing at infinity on the quantum complex plane. It is a subalgebra of the crossed product of the algebra of the continuous functions vanishing at infinity on the half line and the group of integers. Its unitization is considered as the C*-algebra of continuous functions on a quantum 2-sphere. Differences between this construction and the construction of Podles spheres will be highlighted. Finally, the K-theory and K-homology of the new quantum 2-sphere will be discussed.
ELMAR WAGNER (Universidad Michoacana de San Nicolas de Hidalgo, Morelia, Mexico)