Derived invariants for gentle algebras via cleft-extensions

Abstract: In the representation theory of algebras, the search for derived invariants is a central problem. The main result of this paper proves that for two derived equivalent gentle algebras, $A$ and $B$, that satisfy certain conditions, the new gentle algebras, $C_A$ and $C_B$---obtained by applying a cycle-invariant cleft extension to their respective quotient algebras---are also derived equivalent.