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.
|Number of pages||33|
|Journal||Journal of Algebra|
|State||Published - Feb 15 2017|
Bibliographical notePublisher Copyright:
© 2016 Elsevier Inc.
- Cluster-tilted algebra
- Induced module
- Representation theory of associative algebras
- Tilted algebra
ASJC Scopus subject areas
- Algebra and Number Theory