Pith Number

pith:4A2HUOZ2

pith:2026:4A2HUOZ2X4Y44FWA2XSMV3YWVT

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Embedding of pseudotensor category

Wu Zhixiang, Yao Rui

A purely algebraic construction embeds the pseudotensor category M(H) into a tensor category.

arxiv:2605.18369 v1 · 2026-05-18 · math.QA · math.CT · math.RT

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\pithnumber{4A2HUOZ2X4Y44FWA2XSMV3YWVT}

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Record completeness

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2 Internet Archive

3 Author claim open · sign in to claim

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

We realize the embedding functor from pseudotensor category to tensor category in a purely algebraic setting when the pseudotensor category is the category M(H) of left H-modules, which is originally defined by Beilinson and Drinfeld.

C2weakest assumption

That the pseudotensor structure on M(H) admits a purely algebraic embedding into a tensor category whose construction does not rely on the original geometric or analytic features of the Beilinson-Drinfeld definition.

C3one line summary

Realizes algebraic embedding of pseudotensor category M(H) into tensor category and constructs Schur functor plus free object using operads.

References

23 extracted · 23 resolved · 0 Pith anchors

[1] B. Bakalov, A. D'Andrea, V. Kac : Theory of finite pseudoalgebras. Adv. Math. Vol.162 (2001) no.1 1--140 2001

[2] B. Bakalov, A. D' Andrea, V. Kac : Irreducible modules over finite simple Lie pseudoalgebras I. Primitive pseudoalgebras of type W and S. Adv. Math. Vol.204 (2006) 278--346 2006

[3] B. Bakalov, A. D' Andrea, V. Kac : Irreducible modules over finite simple Lie pseudoalgebras II. Primitive pseudoalgebras of type K. Adv. Math. Vol.232 (2013) 188--237 2013

[4] B. Bakalov, A. D' Andrea, V. Kac : Irreducible modules over finite simple Lie pseudoalgebras III. Primitive pseudoalgebras of type H. Adv. Math. Vol.392 (2021) 0001--8708 2021

[5] Bakalov et al 2019

Receipt and verification

First computed	2026-05-20T00:05:57.625363Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e0347a3b3abf31ce16c0d5e4caef16ace7800ddfe2921e7e3c98b3e93a1d1e19

Aliases

arxiv: 2605.18369 · arxiv_version: 2605.18369v1 · doi: 10.48550/arxiv.2605.18369 · pith_short_12: 4A2HUOZ2X4Y4 · pith_short_16: 4A2HUOZ2X4Y44FWA · pith_short_8: 4A2HUOZ2

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/4A2HUOZ2X4Y44FWA2XSMV3YWVT \
  | 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: e0347a3b3abf31ce16c0d5e4caef16ace7800ddfe2921e7e3c98b3e93a1d1e19

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b920f6626faea6f4716369281ccbd6a475336582326d47589bd98a14e887bac0",
    "cross_cats_sorted": [
      "math.CT",
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.QA",
    "submitted_at": "2026-05-18T13:18:41Z",
    "title_canon_sha256": "8045d87db9f4f155c5128409c8591ea975d96f348ee23a378e75d1478b03ffe6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.18369",
    "kind": "arxiv",
    "version": 1
  }
}