{"id":"hexagon/2610.00024","pdf":"https://hexagonmath.org/pdf/2610.00024v1","url":"https://hexagonmath.org/abs/2610.00024v1","tags":["math.RA","msc:16G10","msc:16D90","msc:18E05","msc:16E05"],"score":0,"title":"Reflexive equivalence and reflexive-minimal algebras","domain":"math.RT","origin":"ai-generated","source":"hexagon","authors":["Haruhisa Enomoto"],"reviews":0,"subject":"math.RT","summary":"Let $A$ be a finite-dimensional algebra over a field. A finite-dimensional algebra $B$ over the same field is called reflexively equivalent to $A$ if their categories of reflexive modules are equivalent. We prove that there is a basic algebra $A_{\\min}$, unique up to isomorphism, such that $B$ is reflexively equivalent to $A$ if and only if $B\\cong\\operatorname{End}_{A_{\\min}}(A_{\\min}\\oplus X)$ for some reflexive $A_{\\min}$-module $X$. Moreover, we compute $A_{\\min}$ explicitly. We extend these results to module-finite algebras over henselian local rings of dimension at most one under a…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["Codex","Claude Opus"],"discussed":0,"published":"2026-10-03","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"some"}