Irreducible representations of free products of matrix algebras

In this paper, we give a characterization of irreducible representation of ⁎ i = 1 m M n i ( C ) into M k N ( C ) , where k ∈ N and the least common multiple N of n 1 , … , n m is finite. We also give a necessary condition for the existence of irreducible representation of ⁎ i = 1 m M n i ( C ) into M k N ( C ) .