Module theory over Leavitt path algebras and K-theory

Let k be a field and let E be a finite quiver. We study the structure of the finitely presented modules of finite length over the Leavitt path algebra Lk (E) and show its close relationship with the finite-dimensional representations of the inverse quiver over(E, -) of E, as well as with the class of finitely generated Pk (E)-modules M such that TorqPk (E) (k| E0 |, M) = 0 for all q, where Pk (E) is the usual path algebra of E. By using these results we compute the higher K-theory of the von Neumann regular algebra Qk (E) = Lk (E) Σ- 1, where Σ is the set of all square matrices over Pk (E) which are sent to invertible matrices by the augmentation map ε{lunate} : Pk (E) → k| E0 |. © 2009 Elsevier B.V. All rights reserved.