Derived classification of gentle algebras with two cycles

TL;DR

This paper classifies gentle algebras with two cycles under derived equivalence using combinatorial invariants, providing a list of normal forms for these algebras.

Contribution

It introduces a classification method for gentle algebras with two cycles based on combinatorial invariants and presents a comprehensive list of normal forms.

Findings

Classification of gentle algebras with two cycles under derived equivalence

Construction of combinatorial invariants for these algebras

List of normal forms representing all such algebras

Abstract

We classify gentle algebras defined by quivers with two cycles under derived equivalence in a non degenerate case, by using some combinatorial invariants constructed from the quiver with relations defining these algebras. We also present a list of normal forms; any such algebra is derived equivalent to one of the algebras in the list.