A C*-algebra is called $n$-homogeneous (or n-dimensionally homogeneous) if each irreducible $C^\star$-representation of the algebra is $n$-dimensional.

Jun Tomiyama, Masamichi Takesaki, Applications of fibre bundles to the certain class of $C^\ast$-algebras, Tohoku Math. J. (2) 13:3 (1961) 498-522 eucliddoi

The comparison of the Artin’s theorem on characterization of Azumaya algebras and Tomiyama-Takesaki’s theorem on $n$-homogeneous $C^\ast$-algebras is in chapter 9 of

Edward Formanek, Noncommutative invariant theory, in: Group actions on rings (Brunswick, Maine, 1984), 87–119, Contemp. Math. 43, Amer. Math. Soc. 1985 doi