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.

operator algebras

Audience: researchers in the topic

Quantum Groups Seminar [QGS]

Series comments: This online seminar aims to bring together experts in the area of quantum groups. 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.

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