On the centroid of a Leavitt path algebra.

Abstract

We describe the centroid of some Leavitt path algebras. More precisely, for Leavitt path algebras over a field K, we show that if the algebra is simple, then its centroid is isomorphic to K, and if the algebra is prime, then its centroid is also isomorphic to K, except if the graph is a row-finite comet, in which case the centroid is isomorphic to K[x, x−1].