Resumen de Fusion-stable structures on triangulated categories
Yu Qiu, Xiaoting Zhang
Let G be a fusion category acting on a triangulated category D, in the sense that D is a G-module category. Our motivation example is fusion-weighted species, which is essentially Heng’s construction. We study G-stable tilting, cluster and stability structures on D. In particular, we prove the deformation theorem for G-stable stability conditions. A first application is that Duffield–Tumarkin’s categorification of cluster exchange graphs of finite Coxeter–Dynkin type can be naturally realized as fusionstable cluster exchange graphs. Another application is that the universal cover of the hyperplane arrangements of any finite Coxeter–Dynkin type can be realized as the space of fusion-stable stability conditions for certain ADE Dynkin quiver. This provides an alternative uniform proof of K(π, 1)-conjecture in the finite Coxeter–Dynkin case.
