On derived equivalence classification of gentle two-cycle algebras

TL;DR

This paper classifies gentle two-cycle algebras up to derived equivalence, providing a complete classification for nondegenerate cases and partial results with conjectures for degenerate cases.

Contribution

It offers a comprehensive classification of nondegenerate gentle two-cycle algebras and proposes a conjecture for the degenerate cases.

Findings

Complete classification of nondegenerate gentle two-cycle algebras

Partial classification and conjecture for degenerate cases

Framework for derived equivalence in gentle algebras

Abstract

We classify, up to derived (equivalently, tilting-cotilting) equivalence all nondegenerate gentle two-cycle algebras. We also give a partial classification and formulate a conjecture in the degenerate case.