Work

A graph theoretic model for the derived categories of gentle algebras and their homological bilinear forms

Year: 2026

Type: article

Abstract: We customize the existing models for the bounded derived category of gentle algebras to obtain simple graph theoretic tools to analyze indecomposable objects, Auslander-Reiten triangles, and their interaction with the associated homological bilinear form and the Coxeter transformation. We apply these tools to explore related new and classical derived invariants. We exhibit the non-negativity and Dynkin type of the homological quadratic form of a gentle algebra, classify indecomposable perfect complexes by means of its roots, describe the Coxeter polynomial and relate it with the Avella-Alaminos Geiss invariant. We also derive some consequences for Brauer graph algebras.

Source: Journal of Pure and Applied Algebra

DOI: 10.1016/j.jpaa.2026.108318

Authors: Jesús Arturo Jiménez González, Andrzej Mróz

Institutions: Universidad de Guadalajara, Nicolaus Copernicus University

Language: English

Topic: Algebraic structures and combinatorial models

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,550

OpenAlex ID: W4400517427

FWCI:

Cites: 65

Cited by: 2

Related to: 10