Certain properties of generalized tracially approximated C*-algebras

TL;DR

This paper investigates how specific properties like uniform property Gamma, tracial nuclear dimension, and weak divisibility are preserved when passing from a class of C*-algebras to their unital simple extensions within the WTA Omega class.

Contribution

It demonstrates the preservation of key structural properties in unital simple C*-algebras within the WTA Omega class, extending understanding of their stability under certain algebraic operations.

Findings

Preservation of uniform property Gamma in WTA Omega class.

Maintenance of tracial nuclear dimension at most n.

Retention of weak (m, n)-divisibility property.

Abstract

We show that the following properties of unital ${\rm C^*}$-algebra in a class of $\Omega$ are preserved by unital simple ${\rm C^*}$-algebra in the class of $\rm WTA\Omega$: $(1)$ uniform property $\Gamma$, $(2)$ a certain type of tracial nuclear dimension at most $n$, $(3)$ weakly $(m, n)$-divisible.