On Leavitt path algebras of Hopf graphs

TL;DR

This paper explores the structure of Hopf graphs derived from group and ramification data, and characterizes key algebraic properties of their Leavitt path algebras based on these data.

Contribution

It provides a detailed structural analysis of Hopf graphs and characterizes algebraic properties of their Leavitt path algebras in terms of ramification data and group properties.

Findings

Characterization of Gelfand-Kirillov dimension

Determination of stable rank and simplicity conditions

Criteria for finite dimensional representations

Abstract

In this paper, we provide the structure of Hopf graphs associated to pairs $(G, \mathfrak{r})$ consisting of groups $G$ together with ramification datas $\mathfrak{r}$ and their Leavitt path algebras. Consequently, we characterize the Gelfand-Kirillov dimension, the stable rank, the purely infinite simplicity and the existence of a nonzero finite dimensional representation of the Leavitt path algebra of a Hopf graph via properties of ramification data $\mathfrak{r}$ and $G$.