Injective Presentations of Induced Modules over Cluster-Tilted Algebras

Ralf Schiffler, Khrystyna Serhiyenko

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


Every cluster-tilted algebra B is the relation extension C⋉ExtC2(DC,C) of a tilted algebra C. A B-module is called induced if it is of the form M⊗CB for some C-module M. We study the relation between the injective presentations of a C-module and the injective presentations of the induced B-module. Our main result is an explicit construction of the modules and morphisms in an injective presentation of any induced B-module. In the case where the C-module, and hence the B-module, is projective, our construction yields an injective resolution. In particular, it gives a module theoretic proof of the well-known 1-Gorenstein property of cluster-tilted algebras.

Original languageEnglish
Pages (from-to)447-470
Number of pages24
JournalAlgebras and Representation Theory
Issue number2
StatePublished - Apr 1 2018

Bibliographical note

Funding Information:
The authors were supported by the NSF CAREER grant DMS-1254567 and by the University of Connecticut. The second author was also supported by the NSF Postdoctoral fellowship MSPRF-1502881.

Publisher Copyright:
© 2017, Springer Science+Business Media B.V.


  • Cluster-tilted algebra
  • Coinduction
  • Induction
  • Relation extension

ASJC Scopus subject areas

  • Mathematics (all)


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