Some cluster tilting modules for weighted surface algebras

Abstract

Non-singular weighted surface algebras satisfy the necessary condition found in [6] for existence of cluster tilting modules. We show that any such algebra whose Gabriel quiver is bipartite, has a module satisfying the necessary ext vanishing condition. We show that it is 3-cluster tilting precisely for the non-singular triangular or spherical algebras but not for any other weighted surface algebra with bipartite Gabriel quiver.