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We show that E is a finite graph with no sinks if and only if 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))). When k is a field and rank(kÃ) < â, 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(kÃ)+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.
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