Extensions of the reduced group C*-algebra of a free product of amenable groups

TL;DR

This paper investigates the structure of extensions of reduced group C*-algebras for free products of amenable groups, showing they form a calculable group via KK-theory, advancing understanding in operator algebra extensions.

Contribution

It establishes that the extension classes form a group computable through KK-theory for free products of amenable groups, extending previous results to a broader class of groups.

Findings

Extension classes form a calculable group via KK-theory.

The group structure is valid when extensions are considered modulo asymptotic splitting.

Results apply to free products of countable amenable groups.

Abstract

We prove that the unitary equivalence classes of extensions of C*_r(G) by any sigma-unital stable C"-algebra, taken modulo extensions which split via an asymptotic homomorphism, form a group which can be calculated from the universal coefficient theorem of KK-theory when G is a free product of a countable collection of amenable groups.