Compact Lie group actions with continuous Rokhlin property

TL;DR

This paper investigates the continuous Rokhlin property in C*-dynamical systems with compact Lie group actions, utilizing equivariant KK-theory and quantum groups to classify Kirchberg G-algebras.

Contribution

It introduces a classification framework for Kirchberg G-algebras under compact Lie group actions with the Hodgkin condition, using advanced KK-theory techniques.

Findings

Determined KK-equivalence classes for these systems.

Provided a classification of Kirchberg G-algebras.

Applied equivariant KK-theory and quantum group methods.

Abstract

In this paper, we study continuous Rokhlin property of $\mathrm{C}^*$-dynamical systems using techniques of equivariant $\mathrm{KK}$-theory and quantum group theory. In particular, we determine the $\mathrm{KK}$-equivalence class and give a classification of Kirchberg $G$-algebras when the $G$ is a compact Lie group with Hodgkin condition.