Repetitive equivalences and good Wakamatsu-tilting modules

TL;DR

This paper demonstrates that a good Wakamatsu-tilting module induces an equivalence between the stable categories of repetitive algebras of two rings, revealing a deep connection in their module categories.

Contribution

It establishes a new equivalence between stable categories of repetitive algebras via good Wakamatsu-tilting modules, extending the understanding of module category relationships.

Findings

Equivalence between stable categories of repetitive algebras of R and S

Use of good Wakamatsu-tilting modules to induce category equivalences

Extension of tilting theory in the context of repetitive algebras

Abstract

Let $R$ be a ring and $T$ be a good Wakamatsu-tilting module with $S$ the endomorphism ring. We prove that $T$ induces an equivalence between stable categories of repetitive algebras of $R$ and $S$.