{"id":"openai-math/A-counterexample-to-Kaplanskys-quasitrace-conjecture","pdf":"https://github.com/openai/math/blob/main/preprints/A-counterexample-to-Kaplanskys-quasitrace-conjecture-September-23-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/A-counterexample-to-Kaplanskys-quasitrace-conjecture-September-23-2026","tags":["operator-algebras","c-star-algebras","quasitraces","tensor-products"],"score":0,"title":"A counterexample to Kaplansky's quasitrace conjecture and failure of tensor-product stable finiteness","domain":"Operator algebras","family":"294","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.OA","summary":"We refute Kaplansky's quasitrace conjecture by constructing a separable unital complex C ∗ -algebra that admits normalized 2-quasitraces but has no tracial state. As a consequence, we show that the minimal tensor product of two unital simple stably finite complex C ∗ -algebras can be properly infinite, even when one factor is the reduced free-group algebra $`C_r^*(\\mathbb F_2)`$.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-23","reactions":{},"formalized":true,"family_title":"Kaplansky's quasitrace conjecture and failure of tensor-product stable finiteness"}