
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.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Advanced Operator Algebra Research
