Pith Number

pith:MCGJRPIL

pith:2026:MCGJRPILD4NCL65QVAT5SW7MJV

not attested not anchored not stored refs resolved

Restricted quantum groups as graded Hopf algebras

Giovanni Felder, Jelena Ani\'c

A π²-grading on Hopf algebras turns their finite-dimensional representations into a rigid monoidal category equipped with a fibre functor to π-graded vector spaces.

arxiv:2605.15909 v1 · 2026-05-15 · math.QA · math.RT

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\pithnumber{MCGJRPILD4NCL65QVAT5SW7MJV}

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4 Citations open

5 Replications open

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

The finite dimensional representations of a π²-graded Hopf algebra form a rigid monoidal category with a fibre functor to the category of π-graded vector spaces.

C2weakest assumption

The proposed definition of π²-grading by the double groupoid of commutative diagrams of a finite groupoid π is compatible with the Hopf algebra axioms in a manner that preserves the rigid monoidal structure on representations (as introduced in the abstract).

C3one line summary

Introduces π²-graded Hopf algebras whose finite-dimensional representations form rigid monoidal categories with a fiber functor to π-graded vector spaces, with main examples from restricted quantum groups in Andrews-Baxter-Forrester and Jimbo-Miwa-Okado models.

References

47 extracted · 47 resolved · 2 Pith anchors

[1] Quantumq-Langlands corre- spondence 2018 · doi:10.1090/mosc/278.url:https://doi.org/10.1090/mosc/278

[2] arXiv 1604.00423 2016

[3] Quasimap counts and Bethe eigen- functions 2017 · doi:10.17323/1609-

[4] Eight-vertex SOS model and generalized Rogers-Ramanujan-type identities 1984 · doi:10.1007/bf01014383.url:

[5] Hidden symmetries of 4DN= 2 gauge theories 2025

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:01:24.992873Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

608c98bd0b1f1a25fbb0a827d95bec4d4a3da3d1fcfbfece0240cca05b26499f

Aliases

arxiv: 2605.15909 · arxiv_version: 2605.15909v1 · doi: 10.48550/arxiv.2605.15909 · pith_short_12: MCGJRPILD4NC · pith_short_16: MCGJRPILD4NCL65Q · pith_short_8: MCGJRPIL

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/MCGJRPILD4NCL65QVAT5SW7MJV \
  | 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: 608c98bd0b1f1a25fbb0a827d95bec4d4a3da3d1fcfbfece0240cca05b26499f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5e84992126f07873bedaee0654c0dd939dcd976f5c790793a8f7d15c85500a0c",
    "cross_cats_sorted": [
      "math.RT"
    ],
    "license": "http://creativecommons.org/licenses/by-sa/4.0/",
    "primary_cat": "math.QA",
    "submitted_at": "2026-05-15T12:46:11Z",
    "title_canon_sha256": "136a056902fad8a005ad94908098b727fcbc7350ce8633b968c8869750142cba"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.15909",
    "kind": "arxiv",
    "version": 1
  }
}