Tambara-Yamagami, loop groups, bundles and KK-theory

Hopf Algebra Extensions of Group Algebras and Tambara-yamagami Categories

We determine the structure of Hopf algebras that admit an extension of a group algebra by the cyclic group of order 2. We study the corepresentation theory of such Hopf algebras, which provide a generalization, at the Hopf algebra level, of the so called Tambara-Yamagami fusion categories. As a byproduct, we show that every semisimple Hopf algebra of dimension < 36 is necessarily group-theoreti...

Loop Groups and Holomorphic Bundles

This paper considers the links between the geometry of the various flag manifolds of loop groups and bundles over families of rational curves. Aa an application, a stability result for the moduli on a rational ruled surface of G-bundles with additional flag structure along a line is proven for any reductive group; this gives the corresponding stability statement for any compact group K for the ...

Equivariant KK-theory and noncommutative index theory

KK-Equivalence and Continuous Bundles of C*-Algebras

A structural description is given of the separable C∗-algebras that are contractible in KK-theory or E-theory. Subsequently it is shown that two separable C∗-algebras, A and B, are KK-equivalent if and only if there is a bundle of separable C∗-algebras over [0, 1] which is piecewise trivial with no more than six points of non-triviality such that the kernel of each fiber map is KK-contractible,...

L-index theorems, KK-theory, and connections

Let M be a compact manifold. and D a Dirac type differential operator on M . Let A be a C ∗-algebra. Given a bundle W of A-modules over M (with connection), the operator D can be twisted with this bundle. One can then use a trace on A to define numerical indices of this twisted operator. We prove an explicit formula for this index. Our result does complement the Mishchenko-Fomenko index theorem...