Pith Number

pith:S77X7642

pith:2026:S77X7642XUT74DFTMIGVBA4TWK

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Varieties of initial dialgebras and some of their Koszul dual operads

Abdenacer Makhlouf, Aigerim Dauletiyarova, Bauyrzhan Sartayev

For any variety of algebras, a universal algorithm constructs the subvariety of initial dialgebras from which the original algebras can be recovered.

arxiv:2601.16619 v3 · 2026-01-23 · math.RA

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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

For a given variety Var, we present a universal algorithm for constructing a subvariety of Var-dialgebras from which one can recover an algebra belonging to Var. Such a subvariety is called the variety of initial Var-dialgebras.

C2weakest assumption

That a universal algorithm exists which, for arbitrary Var, produces a subvariety of dialgebras allowing recovery of an algebra in Var, without additional restrictions on the identities defining Var.

C3one line summary

A universal algorithm constructs the variety of initial dialgebras for any given variety Var, with bases provided for the free initial Lie and associative dialgebras.

References

15 extracted · 15 resolved · 0 Pith anchors

[1] Albert version 4.0M6; https://web.osu.cz/∼Zusmanovich/soft/albert/

[2] A. Dauletiyarova, B. K. Sartayev, Basis of the free noncommutative Novikov algebra, Journal of Algebra and Its Applications, 2025, 24(12), 2550292 2025

[3] V. Dotsenko, B. Zhakhayev, Distributive lattices of varieties of Novikov algebras, Manuscripta Mathematica, 2025, 176(2), 29 2025

[4] V. Dotsenko, W. Heijltjes. Gr¨ obner bases for operads, http://irma.math.unistra.fr/dotsenko/operads.html, 2019 2019

[5] X. Gao, L. Guo, Z. Han, Y. Zhang, Rota-Baxter operators, differential operators, pre- and Novikov structures on groups and Lie algebras, Journal of Algebra, 684 (2025), 109–148 2025

Formal links

1 machine-checked theorem link

Receipt and verification

First computed	2026-05-20T14:03:24.529931Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

97ff7ffb9abd27fe0cb3620d508393b28a247d927111daec46ebde320dbf3162

Aliases

arxiv: 2601.16619 · arxiv_version: 2601.16619v3 · doi: 10.48550/arxiv.2601.16619 · pith_short_12: S77X7642XUT7 · pith_short_16: S77X7642XUT74DFT · pith_short_8: S77X7642

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/S77X7642XUT74DFTMIGVBA4TWK \
  | 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: 97ff7ffb9abd27fe0cb3620d508393b28a247d927111daec46ebde320dbf3162

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ccfc6e079168a815f8318c05760d59169b5db50f6674c7ab90c8cbce0e7e87db",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RA",
    "submitted_at": "2026-01-23T10:18:05Z",
    "title_canon_sha256": "8cb2cab3b85a510e3c9ff0750e72704511acdc529f7dad0236b00796e52551a6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2601.16619",
    "kind": "arxiv",
    "version": 3
  }
}