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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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