Free path groupoid grading on Leavitt path algebras

TL;DR

This paper introduces a new grading structure for Leavitt path algebras using free path groupoids, providing a framework to analyze their isomorphisms that preserve generators.

Contribution

It presents a novel free path groupoid grading on Leavitt path algebras and characterizes isomorphisms that preserve this grading and generators.

Findings

Leavitt path algebras can be realized as partial skew groupoid rings.

The free path groupoid grading helps classify algebra isomorphisms.

This approach advances understanding of algebraic symmetries and structure.

Abstract

In this work we realize Leavitt path algebras as partial skew groupoid rings. This yields a free path groupoid grading on Leavitt path algebras. Using this grading we characterize free path groupoid graded isomorphisms of Leavitt path algebras that preserves generators.