Module theory over Leavitt path algebras and K-theory

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Abstract

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 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)Σ1, 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|.

MSC

Primary
16D70
Secondary
16D90
16E20
19D50

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