%0 Journal Article
%T Isomorphisms between Leavitt algebras and their matrix rings
%A G. Abrams
%A P. N. ¨¢nh
%A E. Pardo
%J Mathematics
%D 2006
%I arXiv
%X Let $K$ be any field, let $L_n$ denote the Leavitt algebra of type $(1,n-1)$ having coefficients in $K$, and let ${\rm M}_d(L_n)$ denote the ring of $d \times d$ matrices over $L_n$. In our main result, we show that ${\rm M}_d(L_n) \cong L_n$ if and only if $d$ and $n-1$ are coprime. We use this isomorphism to answer a question posed in \cite{PS} 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.
%U http://arxiv.org/abs/math/0612552v2