Moduli of representations of Leavitt path algebras

TL;DR

This paper develops a framework for classifying and constructing moduli spaces of irreducible representations of Leavitt path algebras using quiver algebra techniques, extending existing methods to a broader class of graphs.

Contribution

It establishes an equivalence of categories between certain subcategories of representations of Leavitt path algebras and quiver algebras, and constructs moduli spaces for irreducible classes.

Findings

Equivalence of categories between Rep(A) and Rep(L)

Definition of a dimension function on Rep(L)

Construction of moduli spaces for irreducible representations

Abstract

We transpose Jones' technology and the authors' C*-algebraic techniques to study representations of the Leavitt path algebra L (over an arbitrary row-finite graph) by using its quiver algebra A. We establish an equivalence of categories between certain full subcategories of Rep(A) and Rep(L) that preserves irreducibility and indecomposability. We define a dimension function on Rep(L), and for each finite dimension we provide a moduli space for the irreducible classes by transporting structures of King and Nakajima on quiver representations. Our techniques are both explicit and functorial.