{"id":"openai-math/A-Torsion-Free-Counterexample-to-the-Kadison-Kaplansky-Projection-Conjecture","pdf":"https://github.com/openai/math/blob/main/preprints/A-Torsion-Free-Counterexample-to-the-Kadison-Kaplansky-Projection-Conjecture-September-23-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/A-Torsion-Free-Counterexample-to-the-Kadison-Kaplansky-Projection-Conjecture-September-23-2026","tags":["operator-algebras","group-c-star-algebras","functional-analysis"],"score":0,"title":"A torsion-free counterexample to the Kadison–Kaplansky projection conjecture","domain":"Operator algebras","family":"285","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.OA","summary":"We construct a finitely generated torsion-free discrete group whose reduced group C ∗ -algebra contains a projection other than zero and the identity. This disproves the Kadison–Kaplansky projection conjecture.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-23","reactions":{},"formalized":false,"family_title":"Counterexamples to Baum–Connes and Kadison–Kaplansky"}