Induced and coinduced modules over cluster-tilted algebras

Ralf Schiffler, Khrystyna Serhiyenko

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


We propose a new approach to study the relation between the module categories of a tilted algebra C and the corresponding cluster-tilted algebra B=C⋉E. This new approach consists of using the induction functor −⊗CB as well as the coinduction functor D(B⊗CD−). We show that DE is a partial tilting and a τ-rigid C-module and that the induced module DE⊗CB is a partial tilting and a τ-rigid B-module. Furthermore, if C=EndAT for a tilting module T over a hereditary algebra A, we compare the induction and coinduction functors to the Buan-Marsh-Reiten functor HomCA (T,−) from the cluster-category of A to the module category of B. We also study the question as to which B-modules are actually induced or coinduced from a module over a tilted algebra.

Original languageEnglish
Pages (from-to)226-258
Number of pages33
JournalJournal of Algebra
StatePublished - Feb 15 2017

Bibliographical note

Publisher Copyright:
© 2016 Elsevier Inc.


  • Cluster-tilted algebra
  • Induced module
  • Representation theory of associative algebras
  • Tilted algebra

ASJC Scopus subject areas

  • Algebra and Number Theory


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