The self-injective cluster-tilted algebras
We are going to determine the self-injective cluster-tilted algebras. All are of finite representation type and special biserial. There are two different classes. The first class are the self-injective serial (or Nakayama) algebras with n >= 3 simple modules and Loewy length n-1. The second class of algebras has an even number 2m of simple modules; m indecomposable projective modules have length 3, the remaining m have length m + 1.
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