---
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.'
address:
- 'Graduate School of Mathematical Science, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8914, Japan'
- 'Graduate School of Mathematical Science, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8914, Japan'
author:
- Yuki Arano
- Yosuke Kubota
bibliography:
- 'bibABC.bib'
- 'bibDEFG.bib'
- 'bibHIJK.bib'
- 'bibLMN.bib'
- 'bibOPQR.bib'
- 'bibSTUV.bib'
- 'bibWXYZ.bib'
- 'arXiv.bib'
- 'AtiyahSegal.bib'
title: Compact Lie group actions with continuous Rokhlin property
---

Introduction
============

After the initial work by Connes [@MR0388117], the study of group actions on ${\mathrm{C}^*}$-algebras and von Neumann algebras, particularly their classification, is a fundamental subject in the theory of operator algebras, as well as the classification of operator algebras themselves. In this paper, we focus on actions of compact Lie groups on ${\mathrm{C}^*}$-algebras.

In the study of von Neumann algebras, the classification of compact group actions on factors are studied in Kawahigashi-Takesaki [@MR1156672], Masuda-Tomatsu [@MR2578461] and so on. In the context of 