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Non-stable $$K$$-theory for Leavitt path algebras. (English) Zbl 1332.16003
Summary: 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 P. Ara, M. A. Moreno and E. Pardo [Algebr. Represent. Theory 10, No. 2, 157-178 (2007; Zbl 1123.16006)] in which they computed the monoid $$\mathcal V[L_K(E)]$$ of a Leavitt path algebra over a countable row-finite directed graph.

##### MSC:
 16E20 Grothendieck groups, $$K$$-theory, etc. 16D70 Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) 46L80 $$K$$-theory and operator algebras (including cyclic theory) 16G20 Representations of quivers and partially ordered sets 46L05 General theory of $$C^*$$-algebras 05C25 Graphs and abstract algebra (groups, rings, fields, etc.)
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