On the gauge action of a Leavitt path algebra

TL;DR

This paper introduces a new gauge action concept for Leavitt path algebras using group schemes, capturing the complete grading information similarly to graph $C^*$-algebras.

Contribution

It presents a revised gauge action notion based on group schemes that fully encodes the algebra's grading, advancing the understanding of Leavitt path algebra structures.

Findings

Revised gauge action concept based on group schemes

Captures full grading information of Leavitt path algebras

Aligns with gauge actions in graph $C^*$-algebras

Abstract

We introduce a revised notion of gauge action in relation with Leavitt path algebras. This notion is based on group schemes and captures the full information of the grading on the algebra as it is the case of the gauge action of the graph $C^*$-algebra of the graph.