Cluster Structures for 2-calabi-yau Categories and Unipotent Groups
نویسندگان
چکیده
We investigate cluster tilting objects (and subcategories) in triangulated 2-Calabi-Yau categories and related categories. In particular we construct a new class of such categories related to preprojective algebras of non Dynkin quivers associated with elements in the Coxeter group. This class of 2-Calabi-Yau categories contains the cluster categories and the stable categories of preprojective algebras of Dynkin graphs as special cases. For these 2-Calabi-Yau categories we construct cluster tilting objects associated with each reduced expression. The associated quiver is described in terms of the reduced expression. Motivated by the theory of cluster algebras, we formulate the notions of (weak) cluster structure and substructure, and give several illustrations of these concepts. We give applications to cluster algebras and subcluster algebras related to unipotent groups, both in the Dynkin and non Dynkin case.
منابع مشابه
T-structures and torsion pairs in a 2-Calabi-Yau triangulated category
For a Calabi-Yau triangulated category C of Calabi-Yau dimension d with a d−cluster tilting subcategory T , the decomposition of C is determined by the decomposition of T satisfying ”vanishing condition” of negative extension groups, namely, C = ⊕i∈ICi, where Ci, i ∈ I are triangulated subcategories, if and only if T = ⊕i∈ITi, where Ti, i ∈ I are subcategories with HomC(Ti[t],T j) = 0,∀1 ≤ t ≤ ...
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