Pith Number

pith:H55WW2C2

pith:2026:H55WW2C2VUQU6NRCQ5IIFZDD3U

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Continuous categories of endomorphisms associated with $G$-kernels

Marcel Bischoff, Pradyut Karmakar

Continuous categories of endomorphisms of type III factors arise from G-kernels on compact second countable groups.

arxiv:2605.17514 v1 · 2026-05-17 · math.OA · math-ph · math.CT · math.FA · math.MP · math.QA

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Claims

C1strongest claim

We generalize the construction of tensor categories of endomorphisms of a type III factor M associated with a G-kernel, from the case of a discrete group G to that of a compact second countable group.

C2weakest assumption

The approach assumes the existence of a unitary tensor functor from the category of C(G)-modules, realized as square-integrable functions on a measure space, to the category of endomorphisms of M that produces a continuous family for compact second countable G.

C3one line summary

Generalizes discrete G-kernel endomorphism categories to compact groups using a unitary tensor functor from C(G)-modules to produce continuous families of endomorphisms.

References

4 extracted · 4 resolved · 1 Pith anchors

[1] MR3308880 24 [DHR69] S. Doplicher, R. Haag, and J. E. Roberts,Fields, observables and gauge transformations II, Comm. Math. Phys.15(1969), 173–200. [EGNO15] P. Etingof, S. Gelaki, D. Nikshych, and V. 1969

[2] MR3242743 [GLR85] P. Ghez, R. Lima, and J. E. Roberts,W∗-categories, Pacific J. Math.120(1985), no. 1, 79–109. MR808930 [Haa75] U. Haagerup,The standard form of von Neumann algebras, Math. Scand.37(19 1985

[3] A Cuntz algebra approach to the classification of near-group categories 2015 · arXiv:1512.04288

[4] [Sut80] C. E. Sutherland,Cohomology and extensions of von Neumann algebras. II, Publ. Res. Inst. Math. Sci.16(1980), no. 1, 135–174. MR574031 Email address:mrclbschff@gmail.com Sam Houston State Unive 1980

Formal links

1 machine-checked theorem link

Receipt and verification

First computed	2026-05-20T00:04:43.199441Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3f7b6b685aad214f3622875082e463dd126e30d91fd0cde309e97015890033e1

Aliases

arxiv: 2605.17514 · arxiv_version: 2605.17514v1 · doi: 10.48550/arxiv.2605.17514 · pith_short_12: H55WW2C2VUQU · pith_short_16: H55WW2C2VUQU6NRC · pith_short_8: H55WW2C2

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/H55WW2C2VUQU6NRCQ5IIFZDD3U \
  | 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: 3f7b6b685aad214f3622875082e463dd126e30d91fd0cde309e97015890033e1

Canonical record JSON

{
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    "abstract_canon_sha256": "b6392093bdfe48bbdbec5222d952e57f81f98b5a55f4f15d2a8c933022dbb417",
    "cross_cats_sorted": [
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      "math.CT",
      "math.FA",
      "math.MP",
      "math.QA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2026-05-17T15:59:19Z",
    "title_canon_sha256": "45591b3b607491308b9746e5d9e96ea8c28a57ea69934dcb078808ca823c382a"
  },
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  "source": {
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    "kind": "arxiv",
    "version": 1
  }
}