On Leavitt path algebras of Hopf graphs

Abstract

In this paper, we provide the structure of Leavitt path algebras of Hopf graphs associated to pairs (G, r) consisting of groups G together with ramification datas r. 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 r and G.