{"id":"openai-math/A-Torsion-Free-Group-Algebra-That-Is-Not-Directly-Finite","pdf":"https://github.com/openai/math/blob/main/preprints/A-Torsion-Free-Group-Algebra-That-Is-Not-Directly-Finite-October-4-2026/direct-finiteness.pdf","url":"https://github.com/openai/math/tree/main/preprints/A-Torsion-Free-Group-Algebra-That-Is-Not-Directly-Finite-October-4-2026","tags":["group-algebras","ring-theory","finite-presentations"],"score":0,"title":"A Torsion-Free Group Algebra That Is Not Directly Finite","domain":"Algebra","family":"197","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.RA","summary":"We construct a finitely presented torsion-free counterexample to Kaplansky's direct finiteness conjecture over the field of two elements. The group admits a finite two-dimensional classifying complex.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-04","reactions":{},"formalized":false,"family_title":"A torsion-free group algebra that is not directly finite"}