Type I W*-algebra is the one in which every nonzero central projection contains abelian subprojection.
($*$) Author in [1] defines type $I_{n}$ W*-algebra as type I W*-algebra that has $n$ nonzero abelian mutually orthogonal projections with sum 1. They call them n-homogeneous.
($**$) Meanwhile n-homogenous C*-algebra is by known definition the one whose each irreducible representation is n-dimensional.
Could someone give me hint/tell me where the proof is on how is W*-algebra that is n-homogeneous by ($**$) also n-homogeneous by ($*$) ?
[1] C*-algebras and W*-algebras