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Paper   IPM / M / 16479
School of Mathematics
  Title:   Algebraic Cuntz-Krieger algebras
  Author(s):  Alireza Nasr-Isfahani
  Status:   Published
  Journal: J. Aust. Math. Soc.
  Vol.:  109
  Year:  2020
  Pages:   93-111
  Supported by:  IPM
  Abstract:
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(k×) < ∞, 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×)+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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