Archiv der Mathematik

, Volume 91, Issue 3, pp 218–225 | Cite as

The self-injective cluster-tilted algebras

  • Claus Michael Ringel


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.


Cluster-tilted algebras self-injective algebras biserial algebras 

Mathematics Subject Classification (2000).

16D50 16G10 16G20 16G60 16G70 16L60 18E30 


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Copyright information

© Birkhaeuser 2008

Authors and Affiliations

  1. 1.Fakultät für MathematikUniversität BielefeldBielefeldGermany

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