2025/10/17 by Liping Li, Li, Liping
Mathematics · #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2510.15348
openalex publication_date 2025/10/17 · openalex created_date 2025/10/21 · openalex updated_date 2026/07/28
Given an infinite set Ω and a ring R as well as a group G acting on them, we show that G and a subgroup H share the same canonical relational structure on Ω if and only if the restriction functor gives an equivalence from the category of discrete representations of G to that of H. Moreover, the age of this relational structure satisfies the strong amalgamation property if and only if there is a canonical isomorphism from the category of finite substructures of Ω and embeddings to the opposite category of the orbit category of G. As an application, we prove that finitely generated discrete representations of highly homogeneous groups over the polynomial ring k[Ω] are Noetherian.