Abstract
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 language | English |
|---|---|
| Pages (from-to) | 447-470 |
| Number of pages | 24 |
| Journal | Algebras and Representation Theory |
| Volume | 21 |
| Issue number | 2 |
| DOIs | |
| State | Published - Apr 1 2018 |
Bibliographical note
Publisher Copyright:© 2017, Springer Science+Business Media B.V.
Funding
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.
| Funders | Funder number |
|---|---|
| NSF CAREER | |
| Baxter postdoctoral fellowship | |
| National Science Foundation Arctic Social Science Program | 1254567, DMS-1254567, 1502881 |
| Connecticut 06520 Yale University New Haven Connecticut 06520 | MSPRF-1502881 |
| Fundação para a Ciência e Tecnologia I.P. | PTDC/CCI-BIO/29266/2017 |
Keywords
- Cluster-tilted algebra
- Coinduction
- Induction
- Relation extension
ASJC Scopus subject areas
- General Mathematics