Closure of graded gentle algebras under derived equivalence

Establish that the class of graded gentle algebras is closed under derived equivalence; specifically, show that every graded associative algebra that is perfect-derived equivalent to a graded gentle algebra is itself a graded gentle algebra.

Background

The authors compare the orbifold surface setting with the smooth surface case and recall that closure under derived equivalence is known for ungraded gentle algebras (by Schröer–Zimmermann). They state that the analogous statement for graded gentle algebras is a folklore conjecture, highlighting an open direction closely related to their main conjecture about formal dissections and derived equivalences.

This question seeks to determine whether derived equivalence preserves the gentle structure in the graded context, thereby extending a classical result from the ungraded setting to graded gentle algebras.

References

This contrasts the case of smooth surfaces, where the simplicity of the notion of formal dissection reflects the closure under derived equivalence of gentle algebras which is a result of Schröer and Zimmermann in the ungraded case and a folklore conjecture in the graded case (cf. Conjecture \ref{conjecture:skewgentle} below).

— Fukaya categories of orbifold surfaces in representation theory  (2602.17370 - Barmeier et al., 19 Feb 2026) in Section “Formal generators and graded skew-gentle algebras”