On the structure of triangulated category with finitely many indecomposables
| dc.creator | Amiot, Claire | |
| dc.date | 2006-12-06 | |
| dc.date | 2007-01-12 | |
| dc.date.accessioned | 2026-07-07T07:39:59Z | |
| dc.date.available | 2026-07-07T07:39:59Z | |
| dc.description | We study the problem of classifying triangulated categories with finite-dimensional morphism spaces and finitely many indecomposables over an algebraically closed field. We obtain a new proof of the following result due to Xiao and Zhu: the Auslander-Reiten quiver of such a category is of the form $\mathbb{Z}Δ/G$ where $Δ$ is a disjoint union of simply laced Dynkin diagrams and $G$ a weakly admissible group of automorphisms of $\mathbb{Z}Δ$. Then we prove that for `most' groups $G$, the category $\T$ is standard, \emph{i.e.} $k$-linearly equivalent to an orbit category $\mathcal{D}^b(\modd kΔ)/Φ$. This happens in particular when $\T$ is maximal $d$-Calabi-Yau with $d\geq2$. Moreover, if $\T$ is standard and algebraic, we can even construct a triangle equivalence between $\T$ and the corresponding orbit category. Finally we give a sufficient condition for the category of projectives of a Frobenius category to be triangulated. This allows us to construct non standard 1-Calabi-Yau categories using deformed preprojective algebras of generalized Dynkin type. | |
| dc.identifier | https://arxiv.org/abs/math/0612141 | |
| dc.identifier | http://arxiv.org/abs/math/0612141 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/121657 | |
| dc.subject | Category Theory | |
| dc.subject | Representation Theory | |
| dc.subject | 18E30; 16G70 | |
| dc.title | On the structure of triangulated category with finitely many indecomposables | |
| dc.type | text |