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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 LR(E) is isomorphic to an algebraic Cuntz–Krieger algebra if and only if the C∗ -algebra C∗(E) is unital and rank(K0(C∗(E)))=rank(K1(C∗(E))) . Let k be a field and k× be the group of units of k . When rank(k×)
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