The graded structure of Leavitt path algebras viewed as partial skew group rings

Let E be a directed graph, K K be a field, and F F be the free group on the edges of E . In this work, we use the isomorphism between Leavitt path algebras and partial skew group rings to endow LK(E) L K ( E ) with an F F -grading and study some algebraic properties of this grading. More precisely, we show that graded cleanness, graded unit regularity, and strong grading of LK(E) L K ( E ) are all equivalent.