# Tilting modules and exceptional sequences for leaf quotients of type A zig-zag algebras

## TL;DR

This paper classifies certain tilting modules and exceptional sequences for specific algebra quotients related to type A zig-zag algebras, revealing their structural properties and dualities.

## Contribution

It provides a classification of generalized tilting modules and exceptional sequences for leaf quotients of type A zig-zag algebras, and characterizes these quotients as quasi-hereditary with duality properties.

## Key findings

- Classification of tilting modules and exceptional sequences
- Characterization of quotients as quasi-hereditary with duality
- Insight into the structure of leaf quotients of type A zig-zag algebras

## Abstract

We classify generalized tilting modules and full exceptional sequences for the family of quasi-hereditary quotients of type A zig-zag algebras and for a related family of algebras. We also give a characterization of these quotients as quasi-hereditary algebras with simple preserving duality that are 'close' to self-injective algebras.