On the Representations of Leavitt path algebras

TL;DR

This paper introduces E-algebraic branching systems for graphs, demonstrating their existence and how they induce representations of Leavitt path algebras, with conditions for faithfulness and equivalence of these representations.

Contribution

It defines E-algebraic branching systems and establishes their role in constructing and analyzing representations of Leavitt path algebras, including criteria for faithfulness and equivalence.

Findings

Existence of E-algebraic branching systems for any graph

Conditions for faithfulness of induced representations

Criteria for equivalence of representations

Abstract

Given a graph E we define E-algebraic branching systems, show their existence and how they induce representations of the associated Leavitt path algebra. We also give sufficient conditions to guarantee faithfulness of the representations associated to E-algebraic branching systems and to guarantee equivalence of a given representation (or a restriction of it) to a representation arising from an E-algebraic branching system.