Announcements
PROGRAMME:11 March 2013, 10:15-12:00
ANTIPODES FOR HOPFISH ALGEBRAS
The notion of a Hopfish algebra was introduced by Tang, Weinstein and Zhu. From the viewpoint of non-commutative geometry, it is a very natural generalization of a Hopf algebra. In contrast with Hopf algebras, a Hopfish algebra has as structural maps bimodules rather than homomorphisms of algebras. Although the bialgebra conditions are easily transferred to this setting, the antipode condition is more problematic. The one imposed by Tang, Weinstein and Zhu is motivated and justified by Poisson geometry, but it seems to lack good properties. In this talk, we want to propose a different notion of antipode which has more structural content. This is work in progress, joint with J. Vercruysse.
KENNY DE COMMER (Universite de Cergy-Pontoise)
11 March 2013, 14:15-16:00
K-CYCLES FOR TWISTED K-HOMOLOGY
Let X be a locally finite CW complex with a given twisting datum. Here "twisting datum" is a vector bundle of C* algebras on X in which each fiber is an elementary C* algebra. An elementary C* algebra is a C* algebra A such that there exists a Hilbert space H and an isomorphism of A to the C* algebra of all compact operators on H. This talk will introduce K-cycles for the K-homology of X twisted by the given twisting datum. The abelian group of these K-cycles is isomorphic to the Kasparov twisted K-homology of X. Thus a context for twisted index theory is obtained. Twisted K-cycles are very closely connected to the D-branes of string theory. The above is joint work with A. Carey and B.-L. Wang.
PAUL F. BAUM (Pennsylvania State University, State College, USA / IMPAN)