Folded Gentle Algebras

We use folding techniques to define a new class of gentle-like algebras that generalise the iterated tilted algebras of type $C$ and $\widetilde{C}$, which we call folded gentle algebras. We then show that folded gentle algebras satisfy many of the same remarkable properties of gentle algebras, and that the proof of these properties follows directly from folding arguments. In particular, we classify the indecomposable modules of folded gentle algebras in terms symmetric and asymmetric string and band modules. We classify the Auslander-Reiten sequences over these algebras, showing that irreducible morphisms between string modules are given by adding/deleting hooks and cohooks to/from strings. Finally, we show that the class of folded gentle algebras are closed under derived equivalence.