Algebraic cuntz-krieger algebras

Abstract

We show that a directed graph is a finite graph with no sinks if and only if, for each commutative unital ring, the Leavitt path algebra is isomorphic to an algebraic Cuntz-Krieger algebra if and only if the -algebra is unital and. Let be a field and be the group of units of. When rank k×), we show that the Leavitt path algebra is isomorphic to an algebraic Cuntz-Krieger algebra if and only if is unital and. We also show that any unital -algebra which is Morita equivalent or stably isomorphic to an algebraic Cuntz-Krieger algebra, is isomorphic to an algebraic Cuntz-Krieger algebra. As a consequence, corners of algebraic Cuntz-Krieger algebras are algebraic Cuntz-Krieger algebras. © 2019 Australian Mathematical Publishing Association Inc.