Abstract
We compute the monoid $\mathcal{V} [ L_{K} (E) ]$ of isomorphism classes of finitely generated projective modules of a Leavitt path algebra over an arbitrary directed graph. Our result generalizes the result of Ara, Moreno and Pardo in which they computed the monoid $\mathcal{V}[ L_{K} (E) ]$ of a Leavitt path algebra over a countable row-finite directed graph.
Citation
Damon Hay. Marissa Loving. Martin Montgomery. Efren Ruiz. Katherine Todd. "Non-stable $K$-theory for Leavitt path algebras." Rocky Mountain J. Math. 44 (6) 1817 - 1850, 2014. https://doi.org/10.1216/RMJ-2014-44-6-1817
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