K-amenability for amalgamated free products of amenable discrete quantum groups

TL;DR

This paper extends equivariant KK-theory to locally compact quantum groups and proves the K-amenability of amalgamated free products of amenable discrete quantum groups using quantum Bass-Serre trees.

Contribution

It introduces a quantum analogue of Bass-Serre trees and demonstrates K-amenability for amalgamated free products of amenable discrete quantum groups.

Findings

Extended equivariant KK-theory to quantum groups

Proved K-amenability of certain quantum group constructions

Developed quantum Bass-Serre tree framework

Abstract

The basic notions and results of equivariant KK-theory concerning crossed products can be extended to the case of locally compact quantum groups. We recall these constructions and prove some usefull properties of subgroups and amalgamated free products of discrete quantum groups. Using these properties and a quantum analogue of the Bass-Serre tree, we establish the K-amenability of amalgamated free products of amenable discrete quantum groups.