On Leavitt Path Algebras of Hopf Graphs

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.