Delooping Level of Nakayama algebras

TL;DR

This paper provides a new proof of the equality between finitistic dimension and delooping level in Nakayama algebras, utilizing syzygy filtration, and characterizes Nakayama algebras with finitistic dimension one.

Contribution

It offers an alternative proof of a recent result and characterizes Nakayama algebras with finitistic dimension one using syzygy filtration.

Findings

Proves the equality between finitistic dimension and delooping level for Nakayama algebras.

Provides a characterization of Nakayama algebras with finitistic dimension one.

Utilizes syzygy filtration method in the proof.

Abstract

We give another proof of the recent result of Ringel, which asserts equality between the finitistic dimension and delooping level of Nakayama algebras. The main tool is syzygy filtration method introduced in \cite{sen2019}. In particular, we give characterization of the finitistic dimension one Nakayama algebras.