Completions of Leavitt path algebras

TL;DR

This paper introduces a new class of topologies on Leavitt path algebras of finite graphs and decomposes their graded completions into minimal ideals, advancing the structural understanding of these algebras.

Contribution

It presents a novel topological framework for Leavitt path algebras and provides a decomposition of their graded completions into minimal ideals.

Findings

Defined new topologies on Leavitt path algebras

Decomposed graded completions into minimal ideals

Enhanced structural understanding of Leavitt path algebras

Abstract

We introduce a class of topologies on the Leavitt path algebra $L(\Gamma)$ of a finite directed graph and decompose a graded completion $\widehat{L}(\Gamma)$ as a direct sum of minimal ideals.