Some Results on Inner Quasidiagonal $C^{\ast }$-algebras

Abstract

In the current article, we prove the cross product $C^{\ast }$-algebra by a Rokhlin action of finite group on a strongly quasidiagonal $C^{\ast }$-algbra is strongly quasidiagonal again. We also show that a just-infinite $C^{\ast }$-algebra is quasidiagonal if and only if it is inner quasidiagonal. Finally, we compute the topological free entropy dimension in just-infinite $C^{\ast }$-algebras.