Isomorphism of Matrix Algebras over Cuntz Algebras

Abstract

Starting with a Cuntz algebra On constructed by n isometries, we discuss a C*-algebra consisting of elements of a fixed size k square matrix, where the entries of matrix are from the Cuntz algebra 𝒪n. It is surprising to find that if k divides n, the resulting C*-algebra of matrix is isomorphic to the Cuntz algebra 𝒪n. We extend this result to cases where k is larger than n, showing that the same conclusion holds provided that every prime factor of k divides n.