{"id":"openai-math/A-Counterexample-to-the-Group-Ring-Determinant-Conjecture","pdf":"https://github.com/openai/math/blob/main/preprints/A-Counterexample-to-the-Group-Ring-Determinant-Conjecture-September-23-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/A-Counterexample-to-the-Group-Ring-Determinant-Conjecture-September-23-2026","tags":["group-rings","fuglede-kadison-determinant","operator-algebras"],"score":0,"title":"A Counterexample to the Group-Ring Determinant Conjecture","domain":"Algebra","family":"197","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.RA","summary":"We disprove the unrestricted group-ring Determinant Conjecture. We construct a finitely generated group G and a square matrix over $`\\mathbb Z[G]`$ that is invertible over $`\\mathbb Q[G]`$ and has Fuglede–Kadison determinant strictly between zero and one. The logarithmic integral defining the determinant is finite.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-23","reactions":{},"formalized":true,"family_title":"A torsion-free group algebra that is not directly finite"}