Strongly self-absorbing property for inclusions of $C^*$-algebras with a finite Watatani index

TL;DR

This paper investigates how the strongly self-absorbing property of C*-algebras behaves under inclusions with finite Watatani index, introducing a Rokhlin property for conditional expectations.

Contribution

It introduces a Rokhlin property for conditional expectations and studies the permanence of strongly self-absorbing properties under finite Watatani index inclusions.

Findings

Established a Rokhlin property for conditional expectations.

Analyzed permanence of strongly self-absorbing properties in inclusions.

Provided conditions under which these properties are preserved.

Abstract

Let $P \subset A$ be a inclusion of unital C*-algebras and $E\colon A \to P$ be a conditional expectation of index finite type. We introduce a Rokhlin property for $E$ and discuss about $\mathcal{D}$-absorbing proeprty, where $\mathcal{D}$ is a separable, unital, strongly self-absorbing C*-algebra. In this paper we consider permanent properties for strongly self-absorbing property under inclusions of unital C*-algebras with a finite Watatani index.