Module theory over Leavitt path algebras and K-theory

AbstractLet 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 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:Pk(E)→k|E0|