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Some cluster tilting modules for weighted surface algebras
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Some cluster tilting modules for weighted surface algebras
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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.
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Cyclic covers and non-orbit 3-representation-finite symmetric algebras
Two explicit symmetric algebras, the 36-dimensional lift A and the 84-dimensional 3-spherical algebra S, are 3-representation-finite but cannot be presented as orbit algebras of repetitive categories.
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