Compact Lie group actions with continuous Rokhlin property

Abstract

In this paper, we study continuous Rokhlin property of ${\mathrm{C}}^{\ast }$-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.

18 pages. This paper is separated from Section 7 of arXiv:1508.06815

References in corpus (4)

• Completely positive maps of order zero
• Every simple higher dimensional noncommutative torus is an AT algebra
• Regularity properties and Rokhlin dimension for compact group actions
• KK-theory of circle actions with the Rokhlin property