Bundles of C*-algebras and the KK(X;-,-)-bifunctor

TL;DR

This paper explores the classification of Z-graded C*-algebra bundles using KK(X; -,-) bifunctor, with applications to Cuntz-Pimsner algebras over spheres, advancing understanding of their K-theoretic invariants.

Contribution

It introduces the use of the KK(X; -,-) bifunctor for classifying Z-graded C*-algebra bundles and applies this to classify Cuntz-Pimsner algebras over spheres.

Findings

Classification achieved via K-theoretical invariants

Application to Cuntz-Pimsner algebras over n-spheres

Emphasis on KK(X; -,-) bifunctor role in classification

Abstract

An overview about C*-algebra bundles with a Z-grading is presented, with particular emphasis on classification questions. In particular, we discuss the role of the representable KK(X ; -, -)-bifunctor introduced by Kasparov. As an application, we consider Cuntz-Pimsner algebras associated with vector bundles, and give a classification in terms of K-theoretical invariants in the case in which the base space is an n-sphere.