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- W2964172532 abstract "We prove that if E and F are graphs with a finite number of vertices and an infinite number of edges, if K is a field, and if L K ( E ) and L K ( F ) are simple Leavitt path algebras, then L K ( E ) is Morita equivalent to L K ( F ) if and only if K 0 alg ( L K ( E ) ) ≅ K 0 alg ( L K ( F ) ) and the graphs E and F have the same number of singular vertices, and moreover, in this case one may transform the graph E into the graph F using basic moves that preserve the Morita equivalence class of the associated Leavitt path algebra. We also show that when K is a field with no free quotients, the condition that E and F have the same number of singular vertices may be replaced by K 1 alg ( L K ( E ) ) ≅ K 1 alg ( L K ( F ) ) , and we produce examples showing this cannot be done in general. We describe how we can combine our results with a classification result of Abrams, Louly, Pardo, and Smith to get a nearly complete classification of unital simple Leavitt path algebras — the only missing part is determining whether the “sign of the determinant condition” is necessary in the finite graph case. We also consider the Cuntz splice move on a graph and its effect on the associated Leavitt path algebra." @default.
- W2964172532 created "2019-07-30" @default.
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- W2964172532 date "2013-06-01" @default.
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- W2964172532 title "Classification of unital simple Leavitt path algebras of infinite graphs" @default.
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- W2964172532 doi "https://doi.org/10.1016/j.jalgebra.2013.03.004" @default.
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