# Irreducible and permutative representations of ultragraph Leavitt path algebras

## TL;DR

This paper characterizes perfect, permutative, irreducible representations of ultragraph Leavitt path algebras, extending Chen's construction and linking representations to branching systems, with improved faithfulness criteria.

## Contribution

It extends Chen's irreducible representation construction to ultragraph Leavitt path algebras and characterizes those from perfect branching systems.

## Key findings

- Complete characterization of perfect, permutative, irreducible representations
- Construction of representations from branching systems
- Improved criteria for faithfulness of representations

## Abstract

We completely characterize perfect, permutative, irreducible representations of an ultragraph Leavitt path algebra. For this we extend to ultragraph Leavitt path algebras Chen's construction of irreducible representations of Leavitt path algebras. We show that these representations can be built from branching system and characterize irreducible representations associated to perfect branching systems. Along the way we improve the characterization of faithfulness of Chen's irreducible representations.