Multi-layer quivers and higher slice algebras

TL;DR

This paper introduces multi-layer quivers and demonstrates how to construct higher slice algebras of infinite type from lower ones using bound quivers, matrix, and tensor algebra methods, establishing categorical equivalences.

Contribution

It presents a novel construction method for higher slice algebras of infinite type from existing n-slice algebras via bound quivers and algebraic operations.

Findings

Constructed (n+1)-slice algebras of infinite type from n-slice algebras.

Established equivalences of module categories with quivers of type  A_{n+1}.

Provided algebraic and categorical frameworks for higher slice algebra construction.

Abstract

In this paper, we introduce multi-layer quiver and show how to construct an $(n+1)$-slice algebras of infinite type from an $n$-slice algebra of infinite type using the bound quivers. This leads to constructing $(n+1)$-slice algebras of infinite type as matrix algebra and as tensor algebra of an $n$-slice algebra and equivalences of their module categories as the module categories of diagram of some quiver of type $\widetilde{A}_{n+1}$.