On ultragraph Leavitt path algebras with finite Gelfand-Kirillov dimension

Abstract

In this article, we prove that every ultragraph Leavitt path algebra is a direct limit of Leavitt path algebras of finite graphs and determine the Gelfand-Kirillov dimension of an ultragraph Leavitt path algebra. We also characterize ultragraph Leavitt path algebras whose simple modules are finitely presented, and show that these algebras have finite Gelfand-Kirillov dimension. Moreover, we construct new classes of simple modules over ultragraph Leavitt path algebras associated with minimal infinite emitters and minimal sinks, which have not appeared in the context of Leavitt path algebras of graphs.