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

2022/08/09 by Gonçalves, Daniel, Orozco, Laura, Pinedo, Héctor
#16S88 #16W50 #Combinatorics (math.CO) #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2208.04739

Abstract

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

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