ALGEBRAIC CUNTZ-KRIEGER ALGEBRAS

We show that a directed graph E is a finite graph with no sinks if and only if, for each commutative unital ring R, the Leavitt path algebra L-R(E) is isomorphic to an algebraic Cuntz-Krieger algebra if and only if the C*-algebra C* (E) is unital and rank(K-0(C* (E))) = rank(K-1(C* (E))). Let k be a field and k(x) be the group of units of k. When rank(k(x)) < infinity, we show that the Leavitt path algebra L-k(E) is isomorphic to an algebraic Cuntz-Krieger algebra if and only if L-k(E) is unital and rank(K-1(L-k (E))) = (rank(k(x)) + 1)rank(K-0(L-k(E))). We also show that any unital k-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.