Fusion-equivariant stability conditions and Morita duality

2023/11/12 by Hannah Dell, Dell, Hannah, Edmund Heng +3 · 1 citation
Mathematics · #14F08 #14L30 (Secondary) #16G20 #18M20 (Primary) #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2311.06857

openalex publication_date 2023/11/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a triangulated category D with an action of a fusion category C, we study the moduli space Stab_C(D) of fusion-equivariant Bridgeland stability conditions on D. The main theorem is that the fusion-equivariant stability conditions form a closed, complex submanifold of the moduli space of stability conditions on D. As an application of this framework to finite group actions on categories, we generalise a result of Macrì--Mehrotra--Stellari by establishing a biholomorphism between the space of G-invariant stability conditions on D and the space of rep(G)-equivariant stability conditions on the equivariant category D^G. We also describe applications to the study of stability conditions associated to McKay quivers and to geometric stability conditions on free quotients of smooth projective varieties.

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