Reflections and torsion theories for selfinjective algebras

TL;DR

This paper introduces reflections for selfinjective algebras via torsion theories from two-term tilting complexes, enabling transformations of Brauer trees into lines, advancing understanding of algebraic structures.

Contribution

It presents a novel concept of reflections for selfinjective algebras and links them to transformations of Brauer trees, offering new tools for algebraic analysis.

Findings

Defined reflections for selfinjective algebras

Connected reflections to transformations of Brauer trees

Provided a method to convert any Brauer tree into a line

Abstract

We introduce the notion of reflections for selfinjective algebras from the point of view of torsion theories induced by two-term tilting complexes. As an application, we determine the transformations of Brauer trees associated with reflections. In particular, we provide a way to transform every Brauer tree into a Brauer line.