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. Received: 28 May 2007