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arXiv · 1204.3366

A note on the isomorphism conjectures for Leavitt path algebras

R. Hazrat
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Abstract

We relate two conjectures which have been raised for classification of Leavitt path algebras. For purely infinite simple unital Leavitt path algebras, it is conjectured that K_0 classifies them completely. For arbitrary Leavitt path algebras, it is conjectured that K^{\gr}_0 classifies them completely \cite{hazann}. We show that for two finite graphs with no sinks (which their associated Leavitt path algebras include the purely infinite simple ones) if their K^{\gr}_0-groups of their Leavitt path algebras are isomorphic then their K_0-groups are isomorphic as well.

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R. Hazrat. 2012-04-16. A note on the isomorphism conjectures for Leavitt path algebras. https://arxiv.org/abs/1204.3366

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