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

Abstract

Abstract Let E be a directed graph, $$\mathbb {K}$$ K be a field, and $$\mathbb {F}$$ 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 $$L_\mathbb {K}(E)$$ L K ( E ) with an $$\mathbb {F}$$ F -grading and study some algebraic properties of this grading. More precisely, we show that graded cleanness, graded unit regularity, and strong grading of $$L_\mathbb {K}(E)$$ L K ( E ) are all equivalent.