Semantic Scholar Open Access 2005 430 sitasi

Cluster-tilted algebras are Gorenstein and stably Calabi–Yau

B. Keller I. Reiten

Lihat Sumber DOI

Abstrak

Abstract We prove that in a 2-Calabi–Yau triangulated category, each cluster tilting subcategory is Gorenstein with all its finitely generated projectives of injective dimension at most one. We show that the stable category of its Cohen–Macaulay modules is 3-Calabi–Yau. We deduce in particular that cluster-tilted algebras are Gorenstein of dimension at most one, and hereditary if they are of finite global dimension. Our results also apply to the stable (!) endomorphism rings of maximal rigid modules of [Christof Geis, Bernard Leclerc, Jan Schroer, Rigid modules over preprojective algebras, arXiv: math.RT/0503324 , Invent. Math., in press]. In addition, we prove a general result about relative 3-Calabi–Yau duality over non-stable endomorphism rings. This strengthens and generalizes the Ext-group symmetries obtained in [Christof Geis, Bernard Leclerc, Jan Schroer, Rigid modules over preprojective algebras, arXiv: math.RT/0503324 , Invent. Math., in press] for simple modules. Finally, we generalize the results on relative Calabi–Yau duality from 2-Calabi–Yau to d-Calabi–Yau categories. We show how to produce many examples of d-cluster tilted algebras.

Topik & Kata Kunci

Mathematics

Penulis (2)

B. Keller

I. Reiten

Format Sitasi

APA MLA BibTeX

Keller, B., Reiten, I. (2005). Cluster-tilted algebras are Gorenstein and stably Calabi–Yau. https://doi.org/10.1016/J.AIM.2006.07.013

Akses Cepat

Lihat di Sumber doi.org/10.1016/J.AIM.2006.07.013

Informasi Jurnal

Tahun Terbit: 2005
Bahasa: en
Total Sitasi: 430×
Sumber Database: Semantic Scholar
DOI: 10.1016/J.AIM.2006.07.013
Akses: Open Access ✓