Finite Dimensional Representations of Leavitt Path Algebras

2016/07/15 by Koç, Ayten, Özaydın, Murad
#FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1607.04622

Abstract

When Γ is a row-finite di(rected )graph we classify all finite dimensional modules of the Leavitt path algebra L(Γ) via an explicit Morita equivalence given by an effective combinatorial (reduction) algorithm on the digraph Γ. The category of (unital) L(Γ)-modules is equivalent to a subcategory of quiver representations of Γ. However the category of finite dimensional representations of L(Γ) is tame in contrast to the finite dimensional quiver representations of Γ which are almost always wild.

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