Derived Equivalence of Surface Algebras in Genus 0 via Graded Equivalence
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- David-Roesler, L. Algebr Represent Theor (2014) 17: 1. doi:10.1007/s10468-012-9384-9
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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.