A graph theoretic model for the derived categories of gentle algebras and their homological bilinear forms
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 forms 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.
Fields of Study & Subjects
Algebraic structures and combinatorial models
Homotopy and Cohomology in Algebraic Topology
Topological and Geometric Data Analysis
Publication details
- Journal / source
- Journal of Pure and Applied Algebra
- Volume
- 230
- Issue
- 9
- Pages
- 108318–108318
- Publication date
- 5 June 2026
- Language
- EN