{"id":"hexagon/2610.00392","pdf":"https://hexagonmath.org/pdf/2610.00392v2","url":"https://hexagonmath.org/abs/2610.00392v2","tags":["msc:16E10","msc:16G60","msc:16G70","Cartan determinant"],"score":0,"title":"Cartan determinants in finite representation type over arbitrary fields","domain":"math.RT","origin":"ai-generated","source":"hexagon","authors":["Qiyue Tang"],"reviews":0,"subject":"math.RT","summary":"Let \\(A\\) be a finite-dimensional representation-finite algebra over an arbitrary field, and let \\(M\\) be a nonzero finite-dimensional right \\(A\\)-module. We prove that \\(\\operatorname{End}_A(M)\\) has Cartan determinant one whenever it has finite global dimension. In particular, the Cartan determinant conjecture holds for representation-finite algebras over arbitrary fields.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-20","reactions":{},"withdrawn":false,"authorship":"mixed","formalized":false,"human_understanding":"some"}