Tracially sequentially-split *-homomorphisms between C*-algebras

Abstract

We define a tracial analog of the notion called a sequentially split *-homomorphisms between C*-algebras due to Barlak and Szabo and show that several important approximation properties related to the classification theory of C*-algebras pass from the target algebra to the domain algebra. Then we show that this framework arises from the tracial Rokhlin properties of a finite group action and inclusion of unital C*-algebras.