Equivariant *-homomorphisms, Rokhlin constraints and equivariant UHF-absorption

TL;DR

This paper classifies equivariant *-homomorphisms and actions of finite groups on C*-algebras with the Rokhlin property, introduces obstructions via the Cuntz semigroup, and proves an equivariant UHF-absorption result.

Contribution

It provides a classification of equivariant *-homomorphisms and actions, and establishes new obstructions and absorption results in the context of C*-dynamical systems.

Findings

Classification of equivariant *-homomorphisms and actions.

Identification of obstructions via the Cuntz semigroup.

Establishment of an equivariant UHF-absorption theorem.

Abstract

We classify equivariant *-homomorphisms between C*-dynamical systems associated to actions of finite groups on C*-algebras with the Rokhlin property. In addition, the given actions are classified. An obstruction is obtained for the Cuntz semigroup of a C*-algebra allowing such an action. We also obtain an equivariant UHF-absorption result.