Tilting modules and exceptional sequences for a family of dual extension algebras

TL;DR

This paper classifies generalized tilting modules and exceptional sequences for a specific dual extension algebra, using a combinatorial model to understand the structure of self-orthogonal modules with standard filtrations.

Contribution

It introduces a new combinatorial framework for classifying tilting modules and exceptional sequences in a class of dual extension algebras.

Findings

Complete classification of generalized tilting modules.

Description of full exceptional sequences.

Development of a combinatorial model for indecomposable self-orthogonal modules.

Abstract

We provide a classification of generalized tilting modules and full exceptional sequences for the dual extension algebra of the path algebra of a uniformly oriented linear quiver modulo the ideal generated by paths of length two with its opposite algebra. For the classification of generalized tilting modules we develop a combinatorial model for the poset of indecomposable self-orthogonal modules with standard filtration with respect to the relation arising from higher extensions.