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Abstract: We obtain isomorphisms between the Leavitt path algebras of
specified graphs. From these isomorphisms he is able to achieve two
ends. First, we show that the K_0 groups of various sets of purely infinite
simple Leavitt path algebras, together with the position of the
identity element in K_0, classify the algebras in these sets up to isomorphism.
Second, we show that the isomorphism between matrix rings over the
classical Leavitt algebras, established previously using number-theoretic
methods, can be re-obtained via appropriate isomorphisms between
Leavitt path algebras.
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