Stable equivalence of Morita type and quotient fusion system

2025/09/29 by Li, Conghui
#20C20 #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2509.24795

Abstract

In this note, we prove that stable equivalences of Morita type between blocks of finite groups induce identification of certain quotient fusion systems under sone assumption. We also collect some related results for separable equivalences.

Citations

• Non-injective inductions and restrictions of modules over finite groups
• On stable equivalences of Morita type and nilpotent blocks
• Non-isomorphic 2-groups with isomorphic modular group algebras
• On the blockwise modular isomorphism problem
• The representation dimension of Hecke algebras and symmetric groups
• Bisets as categories, and tensor product of induced bimodules

Related

• Strong fusion control and stable equivalences
• On stable equivalences with endopermutation source
• Pointed fusion systems of blocks
• Generalized Witt and Morita equivalences
• On automorphisms and focal subgroups of blocks