Details
| Original language | English |
|---|---|
| Pages (from-to) | 277-332 |
| Number of pages | 56 |
| Journal | Journal of algebra |
| Volume | 410 |
| Publication status | Published - 15 Jul 2014 |
Abstract
We provide a far reaching derived equivalence classification of the cluster-tilted algebras of Dynkin type D and suggest standard forms for the derived equivalence classes. We believe that the classification is complete, but some subtle questions remain open. We introduce another notion of equivalence called good mutation equivalence which is slightly stronger than derived equivalence but is algorithmically more tractable, and give a complete classification together with standard forms.
Keywords
- Cartan determinant, Cartan matrix, Cluster tilted algebra, Cluster tilting object, Derived category, Derived equivalence, Dynkin diagram, Finite representation type, Good mutation, Quiver mutation, Tilting complex
ASJC Scopus subject areas
- Mathematics(all)
- Algebra and Number Theory
Cite this
- Standard
- Harvard
- Apa
- Vancouver
- BibTeX
- RIS
In: Journal of algebra, Vol. 410, 15.07.2014, p. 277-332.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Towards derived equivalence classification of the cluster-tilted algebras of Dynkin type D
AU - Bastian, Janine
AU - Holm, Thorsten
AU - Ladkani, Sefi
N1 - Funding Information: This work has been carried out in the framework of the research priority program SPP 1388 Representation Theory of the Deutsche Forschungsgemeinschaft (DFG). We gratefully acknowledge financial support through the grants HO 1880/4-1 and LA 2732/1-1. S. Ladkani was also supported by a European Postdoctoral Institute (EPDI) fellowship.
PY - 2014/7/15
Y1 - 2014/7/15
N2 - We provide a far reaching derived equivalence classification of the cluster-tilted algebras of Dynkin type D and suggest standard forms for the derived equivalence classes. We believe that the classification is complete, but some subtle questions remain open. We introduce another notion of equivalence called good mutation equivalence which is slightly stronger than derived equivalence but is algorithmically more tractable, and give a complete classification together with standard forms.
AB - We provide a far reaching derived equivalence classification of the cluster-tilted algebras of Dynkin type D and suggest standard forms for the derived equivalence classes. We believe that the classification is complete, but some subtle questions remain open. We introduce another notion of equivalence called good mutation equivalence which is slightly stronger than derived equivalence but is algorithmically more tractable, and give a complete classification together with standard forms.
KW - Cartan determinant
KW - Cartan matrix
KW - Cluster tilted algebra
KW - Cluster tilting object
KW - Derived category
KW - Derived equivalence
KW - Dynkin diagram
KW - Finite representation type
KW - Good mutation
KW - Quiver mutation
KW - Tilting complex
UR - http://www.scopus.com/inward/record.url?scp=84900311157&partnerID=8YFLogxK
U2 - 10.1016/j.jalgebra.2014.03.034
DO - 10.1016/j.jalgebra.2014.03.034
M3 - Article
AN - SCOPUS:84900311157
VL - 410
SP - 277
EP - 332
JO - Journal of algebra
JF - Journal of algebra
SN - 0021-8693
ER -