From the homotopy category of projective modules over gentle algebras to poset representations

TL;DR

This paper establishes a new triangulated structure for Bondarenko's category, linking it to the homotopy category of gentle algebras and enabling better understanding of their derived categories.

Contribution

It introduces an alternative triangulated structure for Bondarenko's category, facilitating connections with the homotopy category of gentle algebras.

Findings

New triangulated structure for Bondarenko's category

Connection established between homotopy category and poset representations

Enhanced tools for classifying indecomposable objects

Abstract

In [BCP24], the authors describe a triangulated structure of a quotient of a certain category of representations of posets, nowadays known as the Bondarenko's category. This category was essential in [BM03] for classify all indecomposable objects of the derived category of gentle algebras. In view of this connection with the derived category, which possess a triangulated structure. In this paper, we identify another triangulated structure for Bondarenko's category, allowing us to utilize the functor presented in [BM03]. This functor will establishes a connection between the triangulated structure of the homotopy category of gentle algebras and the new triangulated structure of a quotient of a certain Bondarenko's category.