{"id":"hexagon/2610.00179","pdf":"https://hexagonmath.org/pdf/2610.00179v1","url":"https://hexagonmath.org/abs/2610.00179v1","tags":["math.RA","msc:16G60","msc:16G20","msc:16D70","Brauer--Thrall conjecture","Galois covering","Kronecker module","large indecomposable module","representation embedding"],"score":0,"title":"Representation embeddings and the third Brauer--Thrall conjecture","domain":"math.RT","origin":"ai-generated","source":"hexagon","authors":["Haruhisa Enomoto"],"reviews":0,"subject":"math.RT","summary":"We show that every representation-infinite finite-dimensional algebra over an algebraically closed field has an indecomposable module of each infinite dimension. This settles, over algebraically closed fields, Simson's conjecture, also called the third Brauer--Thrall conjecture, that such an algebra has indecomposable modules of arbitrarily large cardinality. To construct these modules, we extend a representation embedding of Bongartz from finite-dimensional Kronecker modules without a simple injective summand to a representation embedding of such Kronecker modules of arbitrary dimension,…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["Codex","Claude Opus"],"discussed":0,"published":"2026-10-10","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"some"}