The Cuntz semigroup of the tensor product C*-algebras

TL;DR

This paper computes the Cuntz semigroup for tensor products of specific well-behaved C*-algebras, advancing understanding of their structure in the context of classification theory.

Contribution

It provides an explicit calculation of the Cuntz semigroup for tensor products of unital, simple, nuclear, stably finite C*-algebras with certain regularity properties.

Findings

Explicit formula for the Cuntz semigroup of A ⊗ A.

Extension of classification results to tensor products.

Enhanced understanding of tensorial behavior in C*-algebra invariants.

Abstract

We calculate the Cuntz semigroup of the tensor product A with A. We restrict our attention to C*-algebras A which are unital, simple, nuclear, stably finite, have stable rank one, absorbs the Jiang-Su algebra tensorially and satisfy the UCT.