{
  "annotation_id": "1b77c3ce-7e8c-432e-9ab2-81e66275bfb3",
  "date_created": "2026-02-17T05:53:26.427000Z",
  "date_modified": "2026-02-17T05:53:26.427000Z",
  "file_hash": "6f148f3714b7716f5c1ba8cf040751d5b5cb013534c9545a3ddf19ba49751b8d",
  "private": false,
  "record": {
    "abstract": "We show that there exists a completely bounded (c.b. in short) homomorphism $u$ from a $C^*$-algebra $C$ with the lifting property (in short LP) into a QWEP von Neumann algebra $N$ that is not strongly similar to a $*$-homomorphism, i.e. the similarities that ``orthogonalize\" $u$ (which exist since $u$ is c.b.) cannot belong to the von Neumann algebra $N$. Moreover, the map $u$ does not admit any c.b. lifting up into the WEP $C^*$-algebra of which $N$ is a quotient. We can take $C=C^*(G)$ (full $C^*$-algebra) where $G$ is any nonabelian free group and $N= B(H)\\bar \\otimes M$ where $M$ is the von Neumann algebra generated by the reduced $C^*$-algebra of $G$.",
    "arxiv_id": "2601.10654",
    "authors": [
      "Gilles Pisier"
    ],
    "categories": [
      "math.OA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "A note on strong similarity and the Connes embedding problem",
    "url": "https://arxiv.org/abs/2601.10654",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "b8fe4d25-606c-491c-a4e0-dd7e4ef2efd1",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}