A C*-algebra is called -homogeneous (or n-dimensionally homogeneous) if each irreducible -representation of the algebra is -dimensional.
Let be a C-algebra. If the set of pure states of is compact and that of primitive ideal?s which are the kernels of one-dimensional irreducible reprentations forms an open set in the structure space of , then is isomorphic to the C-sum of a finite number of homogeneous C-algebras.
The comparison of the Artin’s theorem on characterization of Azumaya algebras and Tomiyama-Takesaki’s theorem on -homogeneous -algebras is in chapter 9 of
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