{"id":"palomar/PALOMAR-2026-10-23-000004","url":"https://github.com/haruhisa-enomoto/multiplicative-bases-deformations/tree/7b9f39f221d8a420a1531f487a3b93ae6d26ce85","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-23-000004-v1.json","repo":"https://github.com/haruhisa-enomoto/multiplicative-bases-deformations","tags":["math.RT","math.RA","msc:16G60","msc:16G70","msc:16G20","msc:16S80","msc:16E40","representation-theory","finite-dimensional-algebras","formalization"],"score":0,"title":"Multiplicative bases and standardness of representation-finite algebras","trust":"high","domain":"math.RT","source":"palomar","authors":["Haruhisa Enomoto"],"reviews":0,"subject":"math.RT","summary":"A complete Lean 4 formalization, built on Mathlib, of two classical theorems of Bautista, Gabriel, Roiter and Salmerón on finite-dimensional representation-finite algebras over an algebraically closed field. Theorem A: every such algebra, in any characteristic, has a normed multiplicative basis, that is, a basis containing a complete set of primitive orthogonal idempotents, closed under products up to zero, and meeting every power of the Jacobson radical in a basis of that power. Theorem B: every basic such algebra over a field of characteristic different from two is standard, that is, its…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-10-23","reactions":{},"formalized":true,"formalizes":[{"title":"Multiplicative bases and deformations of representation-finite algebras","identifier":"","relationship":"formalizes"}]}