Derived Equivalence in Surface Algebras of Genus 0 via Graded   Equivalence
  We determine some of the derived equivalences of a class of gentle algebras called surface algebras. These algebras are constructed from an unpunctured Riemann surface of genus 0 with boundary and marked points by introducing cuts in internal triangles of an arbitrary triangulation of the surface. In particular, we fix a triangulation of a surface and determine when different cuts produce derived equivalent algebras. 
Lucas David-Roesler
math.RT math.CO math.RA