Pith Number

pith:HCCLMIFW

pith:2024:HCCLMIFWG7Q7EVH6XU5KXQJGCI

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On the Nielsen-Thomsen sequence

Laurent Cantier

Nielsen-Thomsen bases and rotation maps enable comparison of *-homomorphisms at the Hausdorffized algebraic K1 level and yield a new proof that two AT-algebras are non-isomorphic.

arxiv:2412.11975 v4 · 2024-12-16 · math.OA

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Claims

C1strongest claim

These insights enable novel comparison methods for *-homomorphisms at the level of the Hausdorffized algebraic K1-groups, and subsequently the Hausdorffized unitary Cuntz group. We apply our methods to classification via the Hausdorffized unitary Cuntz semigroup. In particular, we present a new proof of the non-isomorphism between two AT-algebras constructed by Gong, Jiang and Li.

C2weakest assumption

The newly introduced notions of Nielsen-Thomsen bases, rotation maps and diagonalisable morphisms correctly capture the properties of the sequence's unnatural splitting and thereby validate the claimed comparison methods (abstract, paragraph 2).

C3one line summary

Develops new algebraic tools for the Nielsen-Thomsen sequence to compare *-homomorphisms at Hausdorffized K1 and Cuntz levels and applies them to C*-algebra classification.

Cited by

1 paper in Pith

Tracially reflexive C*-algebras

Receipt and verification

First computed	2026-06-02T02:04:45.630103Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3884b620b637e1f254febd3aabc12612383afe70231a80c3b0e1057d933a36db

Aliases

arxiv: 2412.11975 · arxiv_version: 2412.11975v4 · doi: 10.48550/arxiv.2412.11975 · pith_short_12: HCCLMIFWG7Q7 · pith_short_16: HCCLMIFWG7Q7EVH6 · pith_short_8: HCCLMIFW

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/HCCLMIFWG7Q7EVH6XU5KXQJGCI \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 3884b620b637e1f254febd3aabc12612383afe70231a80c3b0e1057d933a36db

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "de6684c8b7ddb3fee49cc525552675a1c0a51cddea525a59058955b623139e58",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2024-12-16T16:58:53Z",
    "title_canon_sha256": "93b6e1f8620883fb6610ca07b707637a46bfed6f0c2c82b787745cc6acc49fff"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2412.11975",
    "kind": "arxiv",
    "version": 4
  }
}