Induced and coinduced modules over cluster-tilted algebras

JOURNAL OF ALGEBRA

卷:472

Article

Schiffler, Ralf¹  Serhiyenko, Khrystyna¹ 

[1] Univ Connecticut, Dept Math, Storrs, CT 06269 USA

关键词: Representation theory of associative algebras;    Induced module;    Cluster-tilted algebra;    Tilted algebra;   

DOI  :  10.1016/j.jalgebra.2016.10.009

来源: Elsevier

【 摘 要 】

We propose a new approach to study the relation between the module categories of a tilted algebra C and the corresponding duster-tilted algebra B = C x E. This new approach consists of using the induction functor B as well as the coinduction functor D(B circle plus(c) D). We show that DE is a partial tilting and a tau-rigid C-module and that the induced module DE circle times(C) B is a partial tilting and a tau-rigid B-module. Furthermore, if C = End(A)T for a tilting module T over a hereditary algebra A, we compare the induction and coinduction functors to the Buan-Marsh-Reiten functor Hom(cA) (T, -) from the duster-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. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free