The Reciprocal Kirchberg Algebras

TL;DR

This paper introduces the concept of reciprocality for unital Kirchberg algebras with finitely generated K-groups, linking it to their homotopy theory and bundle structures, and establishes a duality principle for these algebras.

Contribution

It defines the property of reciprocality for Kirchberg algebras and proves its relation to homotopy theory and bundle structure, including a Spanier-Whitehead duality result.

Findings

Reciprocality is closely related to homotopy theory of Kirchberg algebras.

Reciprocal Kirchberg algebras share the same bundle structure.

Spanier-Whitehead duality holds for certain bundles of nuclear UCT C*-algebras.

Abstract

For two unital Kirchberg algebras with finitely generated K-groups, we introduce a property, called reciprocality, which is proved to be closely related to the homotopy theory of Kirchberg algebras. We show the Spanier--Whitehead duality for bundles of separable nuclear UCT C*-algebras with finitely generated K-groups and conclude that two reciprocal Kirchberg algebras share the same structure of their bundles.