A derived equivalence between cluster equivalent algebras

作者：Amiot Claire^*

来源：Journal of Algebra, 2012, 351(1): 107-129.

DOI：10.1016/j.jalgebra.2011.11.009

• Generalized cluster categories
• Derived equivalence
• Tilting theory
• 2-APR-tilting

Let Q be an acyclic quiver. Associated with any element w of the Coxeter group of Q. triangulated categories (Sub) under bar Lambda(w) were introduced in Buan et al. (2009) [BIRS09]. For any reduced expression w of w, the categories (Sub) under bar Lambda(w) are shown to be triangle equivalent to generalized cluster categories C Gamma(w) associated to algebras Gamma(w) of global dimension <= 2 in Amiot et al. (2011) [ART11]. For A(w) satisfying a certain property, called co-c-sortable, other algebras of global dimension 2 are constructed in Amiot (2009) [Ami09] and Amiot et al. (2011) [AIRT11] with a triangle equivalence CA(w) congruent to (Sub) under bar Lambda(w). The main result of this paper is that the algebras Gamma(w) and A(w) are derived equivalent when w is co-c-sortable. The proof constructs explicitly a tilting module using the 2-APR-tilting theory introduced in Iyama and Oppermann (2011) [IO09].

• 出版日期2012-2-1