Quantum Groups Seminar

The seminar topics will cover the theory of quantum groups and related structures in a large sense: Hopf algebras, operator algebras, q-deformations, higher categories and related branches of noncommutative mathematics.

  • More information about the schedule can be found here.
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Speaker: Shintaro Nishikawa (University of Muünster)

Title: Crossed products of representable localization algebras.

Abstract: Let X be a locally compact, Hausdorff space. The representable localization algebra for X was introduced and studied by Willett and Yu. The K-theory of the algebra serves as the representable K-homology of the space X.

Now let G be a second countable, locally compact group and suppose that X is a proper G-space. It turns out that the K-theory of the crossed product by G of the representable localization algebra for X serves as the representable G-equivariant K-homology of the proper G-space X.

The goal of this talk is to describe these facts and roles of the representable localization algebras in the study of the Baum—Connes conjecture.