{"id":"hexagon/2610.00505","pdf":"https://hexagonmath.org/pdf/2610.00505v1","url":"https://hexagonmath.org/abs/2610.00505v1","tags":["math.RA","msc:16G10","msc:16G20","msc:16G60","Auslander--Reiten theory","deformation","mesh category","multiplicative basis","representation-finite algebra"],"score":0,"title":"Multiplicative bases and deformations of representation-finite algebras","domain":"math.RT","origin":"ai-generated","source":"hexagon","authors":["Haruhisa Enomoto"],"reviews":0,"subject":"math.RT","summary":"Bautista, Gabriel, Roiter, and Salmer\\'on proved that every finite-dimensional representation-finite algebra over an algebraically closed field admits a multiplicative basis, in which products of basis elements are zero or basis elements. Outside characteristic two, they also proved that such an algebra is standard: its category of indecomposable modules is presented by its Auslander--Reiten quiver and mesh relations. We give another proof of both theorems. For a basic algebra, grading morphisms between indecomposable modules by powers of the categorical radical and restricting to…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["Codex","Claude Opus","Gemini"],"discussed":0,"published":"2026-10-23","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":true,"formalizations":["https://palomar-registry.org/entry?id=PALOMAR-2026-10-23-000004&version=1"],"human_understanding":"some"}