2 00 6 Isomorphisms between Leavitt Algebras and Their Matrix Rings

Let K be any field, let L n denote the Leavitt algebra of type (1, n − 1) having coefficients in K, and let M d (L n) denote the ring of d × d matrices over L n. In our main result, we show that M d (L n) ∼ = L n if and only if d and n − 1 are coprime. We use this isomorphism to answer a question posed in [14] regarding isomorphisms between various C*-algebras. Furthermore, our result demonstrates that data about the K 0 structure is sufficient to distinguish up to isomorphism the algebras in an important class of purely infinite simple K-algebras.