Pith Number

pith:N6LOLOKI

pith:2025:N6LOLOKIE7XICR56O5TS5YQJLW

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Groupoid models for relative Cuntz-Pimsner algebras of groupoid correspondences

Ralf Meyer

Relative Cuntz-Pimsner algebras arising from groupoid correspondences are themselves groupoid C*-algebras.

arxiv:2506.19569 v3 · 2025-06-24 · math.OA

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Claims

C1strongest claim

We show that the Cuntz-Pimsner algebra for this C*-correspondence relative to an ideal associated to an open invariant subset of the groupoid is again a groupoid C*-algebra for a certain groupoid.

C2weakest assumption

The input is an etale locally compact groupoid equipped with a groupoid correspondence whose induced C*-correspondence admits a relative Cuntz-Pimsner construction with respect to the ideal coming from an open invariant subset.

C3one line summary

The relative Cuntz-Pimsner algebra of a groupoid correspondence is the groupoid C*-algebra of a new groupoid with an explicit description and universal property for actions on topological spaces.

References

25 extracted · 25 resolved · 0 Pith anchors

[1] Thesis, Georg-August- Universität Göttingen, 2015, http://hdl.handle.net/11858/00-1735-0000-0028-87E8-C 2015

[2] Thesis, Georg-August-Universität Göttingen, 2024 2024 · doi:10.53846/goediss-10930

[3] Math.28 (2022), 1329–1364, available athttps://nyjm.albany.edu/j/2022/28-56 2022

[4] Alcides Buss, Rohit Holkar, and Ralf Meyer,A universal property for groupoid C∗-algebras. I, Proc. Lond. Math. Soc. (3)117 (2018), no. 2, 345–375, doi: 10.1112/plms.12131.MR3851326 34 RALF MEYER 2018 · doi:10.1112/plms.12131.mr3851326

[5] Alcides Buss and Ralf Meyer,Inverse semigroup actions on groupoids, Rocky Mountain J. Math. 47 (2017), no. 1, 53–159, doi: 10.1216/RMJ-2017-47-1-53. MR3619758 2017 · doi:10.1216/rmj-2017-47-1-53

Receipt and verification

First computed	2026-05-20T14:03:19.522350Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6f96e5b94827ee8147be77672ee2095d8f61b303b0e51d0f8c01accff9b25bcc

Aliases

arxiv: 2506.19569 · arxiv_version: 2506.19569v3 · doi: 10.48550/arxiv.2506.19569 · pith_short_12: N6LOLOKIE7XI · pith_short_16: N6LOLOKIE7XICR56 · pith_short_8: N6LOLOKI

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/N6LOLOKIE7XICR56O5TS5YQJLW \
  | 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: 6f96e5b94827ee8147be77672ee2095d8f61b303b0e51d0f8c01accff9b25bcc

Canonical record JSON

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    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2025-06-24T12:30:49Z",
    "title_canon_sha256": "72e41655ad91f9b9b3cd1748f6d15e8784528b9c9e0075b68a63a2bfe11f07b3"
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