Finitely presented modules over Leavitt algebras

Abstract

Given a field k and a positive integer n, we study the structure of the finitely presented modules over the Leavitt k-algebra L of type (1, n), which is the k-algebra with a universal isomorphism i : L→L n+1 . The abelian category of finitely presented left L-modules of finite length is shown to be equivalent to a certain subcategory of finitely presented modules over the free algebra of rank n+1, and also to a quotient category of the category of finite dimensional (over k) modules over a free algebra of rank n+1, modulo a Serre subcategory generated by a single module. This allows us to use Schofield's exact sequence for universal localization to compute the K 1 group of a certain von Neumann regular algebra of fractions of L.