Exceptional Sequences and Clusters
نویسنده
چکیده
We show that exceptional sequences for hereditary algebras are characterized by the fact that the product of the corresponding reflections is the inverse Coxeter element in the Weyl group. We use this result to give a new combinatorial characterization of clusters tilting sets in the cluster category in the case where the hereditary algebra is of finite type.
منابع مشابه
Exceptional Sequences, Braid Groups and Clusters
Introduction 1 1. Topological AR-quivers 2 2. Theorem of Brady-Watt and Bessis 3 3. Exceptional sequences 4 3.1. Basic definitions 5 3.2. Braid action on exceptional sequences 6 3.3. Example: Auslander-Reiten translation 7 4. Theorems about exceptional sequences 8 5. Appendix 10 5.1. Example: A2 10 5.2. More general almost split sequences 11 5.3. Bimodule of injectives 11 5.4. Untwisting in sep...
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