Two-term partial tilting complexes over Brauer tree algebras

TL;DR

This paper classifies all indecomposable two-term partial tilting complexes over Brauer tree algebras with multiplicity 1, and applies this to describe two-term tilting complexes over Brauer star algebras, including their endomorphism rings.

Contribution

It provides a complete classification of indecomposable two-term partial tilting complexes over Brauer tree algebras with multiplicity 1, and extends this to Brauer star algebras with explicit endomorphism ring computations.

Findings

Classified all indecomposable two-term partial tilting complexes over Brauer tree algebras with multiplicity 1.

Described all two-term tilting complexes over Brauer star algebras.

Computed endomorphism rings of these tilting complexes.

Abstract

In this paper we describe all indecomposable two-term partial tilting complexes over a Brauer tree algebra with multiplicity 1 using a criterion for a minimal projective presentation of a module to be a partial tilting complex. As an application we describe all two-term tilting complexes over Brauer star algebra and compute their endomorphism rings.