Structure theory of graded regular graded self-injective rings and applications

TL;DR

This paper develops a structure theory for graded regular graded self-injective rings and applies it to classify certain Leavitt path algebras, showing they are of graded type I and identifying their specific class.

Contribution

It introduces a new structure theory for graded regular graded self-injective rings and characterizes Leavitt path algebras of finite graphs within this framework.

Findings

Graded regular graded self-injective Leavitt path algebras are of graded type I.

Such algebras are exactly the graded $\\Sigma$-$V$ Leavitt path algebras.

The paper provides a classification linking ring structure to graph properties.

Abstract

In this paper, we develop structure theory for graded regular graded self-injective rings and apply it in the context of Leavitt path algebras. We show that for a finite graph, graded regular graded self-injective Leavitt path algebras are of graded type I and these are precisely graded $\Sigma$-$V$ Leavitt path algebras.