Graph algebras and the Gelfand-Kirillov dimension.

Abstract

We study some properties of the Gelfand-Kirillov dimension in a non-necessarily unital context. In particular, its Morita invariance when the algebras have local units, and its commutativity with direct limits. We then give some applications in the context of graph algebras, which embraces, among some others, path algebras and Cohn and Leavitt path algebras. In particular we determine the GK-dimension of these algebras in full generality, so extending the main result in [6].