{"id":"openai-math/An-explicit-obstruction-to-nuclear-norm-ultrapower-embeddings","pdf":"https://github.com/openai/math/blob/main/preprints/An-explicit-obstruction-to-nuclear-norm-ultrapower-embeddings-September-23-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/An-explicit-obstruction-to-nuclear-norm-ultrapower-embeddings-September-23-2026","tags":["operator-algebras","c-star-algebras"],"score":0,"title":"An explicit obstruction to nuclear norm-ultrapower embeddings","domain":"Operator algebras","family":"292","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.OA","summary":"We give a negative answer to Kirchberg's norm-ultrapower embedding problem. We construct an explicit separable unital full group C ∗ -algebra that admits no unital embedding into B ω , for any nonzero unital nuclear C ∗ -algebra B and any free ultrafilter ω on ℕ. In particular, it does not embed unitally into $`\\mathcal O_2^\\omega`$.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-23","reactions":{},"formalized":false,"family_title":"Kirchberg's $`\\mathcal O_2`$ norm-ultrapower embedding problem"}