Derived Equivalence in Surface Algebras of Genus 0 via Graded Equivalence

2011/11/20 by David-Roesler, Lucas
#16G20 #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1111.4657

Abstract

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.

Related

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• Algebras from surfaces without punctures
• Derived invariants for surface cut algebras II: the punctured case
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• A geometric model for the module category of a gentle algebra