A Rohlin Type Theorem for Automorphisms of Certain Purely Infinite $C^{\ast}$-Algebras

TL;DR

This paper proves a noncommutative Rohlin type theorem for automorphisms of a specific class of purely infinite simple $C^{ ext{*}}$-algebras, expanding understanding of their automorphism structure.

Contribution

It establishes a Rohlin type theorem for automorphisms of certain purely infinite simple $C^{ ext{*}}$-algebras with trivial $K_1$-groups, a new result in operator algebra theory.

Findings

Proves a noncommutative Rohlin theorem for specific $C^{ ext{*}}$-algebras.

Identifies conditions under which automorphisms satisfy the Rohlin property.

Extends the class of algebras for which Rohlin type theorems are known.

Abstract

We show a noncommutative Rohlin type theorem for automorphisms of a certain class of purely infinite simple $C^{\ast}$-algebras. This class consists of the purely infinite unital simple $C^{\ast}$-algebras which are in the bootstrap category ${\cal N}$ and have trivial $K_{1}$-groups.