Paper Citation Record · LEDGER

Induced structures of averaging commutative and cocommutative infinitesimal bialgebras via a new splitting of perm algebras

As of 21 August 2026, this Paper Citation Record lists 52 of 52 outbound references and 1 inbound Pith citation observation for arXiv:2509.09884.

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pith.paper-citation-record.v1
2509.09884 v1

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measured 52 of 52 reference resolution

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Source: paper_references, paper_reference_links, observed 2026-08-04T18:38:51.089717Z

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Source: scholarly_work_events, retraction_status_cache, observed 2026-08-20T06:33:59.587034+00:00

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Source: paper_references, paper_reference_links, observed 2026-06-27T17:28:30.609864Z

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Source: arxiv_reference, observed 2026-07-03T00:07:28.356914Z

Reference resolution

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Outbound references

Observation 5c987cd2-390b-4497-b5f3-13f401b698f8 · outbound

This paper cites Aguiar, Infinitesimal Hopf algebras, in: New Trends in Hopf Algebra Theory, La Falda, 1999, in:Contemp.

Induced structures of averaging commutative and cocommutative infinitesimal bialgebras via a new splitting of perm algebras Aguiar, Infinitesimal Hopf algebras, in: New Trends in Hopf Algebra Theory, La Falda, 1999, in:Contemp

Reference 1

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Observation 1b3a7cd5-fd13-4da0-99fb-c6f4eced6ed2 · outbound

This paper cites Aguiar, Pre-Poisson algebras,J.

Induced structures of averaging commutative and cocommutative infinitesimal bialgebras via a new splitting of perm algebras Aguiar, Pre-Poisson algebras,J

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Observation be539280-dd25-49dc-9a4a-81ac1aa9e832 · outbound

This paper cites Aguiar, On the associative analog of Lie bialgebras,J.

Induced structures of averaging commutative and cocommutative infinitesimal bialgebras via a new splitting of perm algebras Aguiar, On the associative analog of Lie bialgebras,J

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Observation 74097b5d-e1c7-4d46-8a8e-bea05545e13e · outbound

This paper cites Aguiar, Infinitesimal bialgebras, pre-Lie and dendriform algebras, in: Hopf algebras, inLecture Notes in Pure and Appl.

Induced structures of averaging commutative and cocommutative infinitesimal bialgebras via a new splitting of perm algebras Aguiar, Infinitesimal bialgebras, pre-Lie and dendriform algebras, in: Hopf algebras, inLecture Notes in Pure and Appl

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Observation d6128f28-4964-4eff-ba13-4766b440290d · outbound

This paper cites Bai, Left-symmetric bialgebras and an analogue of the classical Yang-Baxter equation,Comm.

Induced structures of averaging commutative and cocommutative infinitesimal bialgebras via a new splitting of perm algebras Bai, Left-symmetric bialgebras and an analogue of the classical Yang-Baxter equation,Comm

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Observation 278c7dc8-602c-4a70-8bde-50028e403342 · outbound

This paper cites Bai, Double constructions of Frobenius algebras, Connes cocycles and their duality,J.

Induced structures of averaging commutative and cocommutative infinitesimal bialgebras via a new splitting of perm algebras Bai, Double constructions of Frobenius algebras, Connes cocycles and their duality,J

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Observation 46806a97-2a66-4c12-9b5d-fb21c7c2a201 · outbound

This paper cites Bai, An introduction to pre-Lie algebras, in: Algebra and Applications 1: Nonssociative Algebras and Categories, Wiley Online Library (2021) 245-273.

Induced structures of averaging commutative and cocommutative infinitesimal bialgebras via a new splitting of perm algebras Bai, An introduction to pre-Lie algebras, in: Algebra and Applications 1: Nonssociative Algebras and Categories, Wiley Online Library (2021) 245-273

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Observation 8cc70a0c-f22d-4ed4-8c23-eac1889d437e · outbound

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Induced structures of averaging commutative and cocommutative infinitesimal bialgebras via a new splitting of perm algebras Unresolved cited work

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Observation 6e41bf68-5fe3-480f-b721-758941194550 · outbound

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Induced structures of averaging commutative and cocommutative infinitesimal bialgebras via a new splitting of perm algebras Unresolved cited work

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Observation ccfddbe6-bab3-4d8f-9c2c-ac26169c2ac1 · outbound

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Induced structures of averaging commutative and cocommutative infinitesimal bialgebras via a new splitting of perm algebras Unresolved cited work

Reference 10

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Observation 9e18bd5a-3113-4bab-a06f-c5206c88f1b9 · outbound

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Induced structures of averaging commutative and cocommutative infinitesimal bialgebras via a new splitting of perm algebras Unresolved cited work

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Observation 33ce2036-6ca4-4f07-9c65-0349b1507160 · outbound

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Induced structures of averaging commutative and cocommutative infinitesimal bialgebras via a new splitting of perm algebras Unresolved cited work

Reference 12

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Observation 5aa88e28-67cf-404b-b0f2-f8ce2f96a393 · outbound

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Induced structures of averaging commutative and cocommutative infinitesimal bialgebras via a new splitting of perm algebras Birkhoff, Lattices in applied mathematics, II Averaging operators,Proc

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Observation 59e10731-5aa5-4635-a301-81394bc8ba8c · outbound

This paper cites Burde, Left-symmetric algebras, or pre-Lie algebras in geometry and physics,Cent.

Induced structures of averaging commutative and cocommutative infinitesimal bialgebras via a new splitting of perm algebras Burde, Left-symmetric algebras, or pre-Lie algebras in geometry and physics,Cent

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Observation d31518c3-d18d-41d7-99c9-b778a2b544c8 · outbound

This paper cites Chapton, Un endofoncteur de la cat ´egorie des op ´erades, in: Dialgebras and related operads,Lect.

Induced structures of averaging commutative and cocommutative infinitesimal bialgebras via a new splitting of perm algebras Chapton, Un endofoncteur de la cat ´egorie des op ´erades, in: Dialgebras and related operads,Lect

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Observation 7809d7a0-a1c3-4c00-ae35-4812d8ef24cb · outbound

This paper cites Chari and A.

Induced structures of averaging commutative and cocommutative infinitesimal bialgebras via a new splitting of perm algebras Chari and A

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Observation 6aa425c8-ae12-4c3a-8b98-b3ba9ac02783 · outbound

This paper cites Das and S.

Induced structures of averaging commutative and cocommutative infinitesimal bialgebras via a new splitting of perm algebras Das and S

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Observation 8814f8f4-d3c0-42d0-ad88-5e09d26eb587 · outbound

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Induced structures of averaging commutative and cocommutative infinitesimal bialgebras via a new splitting of perm algebras Drinfeld, Halmiltonian structure on the Lie groups, Lie bialgebras and the geometric sense of the classical Yang-Baxter equations,Sov

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Observation 7c72ebdd-897c-4a0a-a455-6b01ce23b47a · outbound

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Induced structures of averaging commutative and cocommutative infinitesimal bialgebras via a new splitting of perm algebras Dzhumadil’daev, Algebras with skew-symmetric identity of degree 3,J

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Observation 7ce3c6e1-fca9-40b5-ae84-e4267879073c · outbound

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Induced structures of averaging commutative and cocommutative infinitesimal bialgebras via a new splitting of perm algebras Dzhumadil’daev and P

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Observation e4c32009-efc7-4d20-b1a9-93ab703e55f1 · outbound

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Induced structures of averaging commutative and cocommutative infinitesimal bialgebras via a new splitting of perm algebras Unresolved cited work

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Observation 2f82f4e9-f7a0-49df-a89c-58e6e7313ab4 · outbound

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Induced structures of averaging commutative and cocommutative infinitesimal bialgebras via a new splitting of perm algebras Gao and T

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Observation 29127469-cf57-4e7d-b472-b57569cfddee · outbound

This paper cites Gelfand and I.

Induced structures of averaging commutative and cocommutative infinitesimal bialgebras via a new splitting of perm algebras Gelfand and I

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Observation 38486c74-f838-4943-8604-8c8200cde7eb · outbound

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Induced structures of averaging commutative and cocommutative infinitesimal bialgebras via a new splitting of perm algebras Unresolved cited work

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Induced structures of averaging commutative and cocommutative infinitesimal bialgebras via a new splitting of perm algebras Guo, Operated semigroups, Motzkin paths and rooted trees,J

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Observation c0ccfbe8-cff1-43ba-a4ae-eae93da808ff · outbound

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Induced structures of averaging commutative and cocommutative infinitesimal bialgebras via a new splitting of perm algebras Deformation families of Novikov bialgebras via differential antisymmetric infinitesimal bialgebras

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Observation bdd15c5d-3067-48ad-82d5-697870314b57 · outbound

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Induced structures of averaging commutative and cocommutative infinitesimal bialgebras via a new splitting of perm algebras Hou, Extending structures for perm algebras and perm bialgebras,J

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Observation 0d827154-4d74-4a6b-accb-24b296ff4b39 · outbound

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Induced structures of averaging commutative and cocommutative infinitesimal bialgebras via a new splitting of perm algebras Kamp ´de F ´eriet, L’etat actuel du probl ´eme de la turbulaence (I and II),La Sci

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Observation 3df40efb-b60c-4820-b8b3-266fd64b9fd9 · outbound

This paper cites Kock, Frobenius Algebras and 2d Topological Quantum Field Theories, Cambridge University Press, Cam- bridge.

Induced structures of averaging commutative and cocommutative infinitesimal bialgebras via a new splitting of perm algebras Kock, Frobenius Algebras and 2d Topological Quantum Field Theories, Cambridge University Press, Cam- bridge

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Observation 0d762f38-5059-4d6e-b57d-5d736aab8633 · outbound

This paper cites Kotov and T.

Induced structures of averaging commutative and cocommutative infinitesimal bialgebras via a new splitting of perm algebras Kotov and T

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Induced structures of averaging commutative and cocommutative infinitesimal bialgebras via a new splitting of perm algebras Kupershmidt, What a classicalr-matrix really is,J

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Observation d94875a4-2909-428d-913f-2ebd34d39e8c · outbound

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Induced structures of averaging commutative and cocommutative infinitesimal bialgebras via a new splitting of perm algebras Lauda and H

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Observation 082b7bb7-9696-43b1-97a3-18a54da79b4a · outbound

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Induced structures of averaging commutative and cocommutative infinitesimal bialgebras via a new splitting of perm algebras Lavau, Tensor hierarchies and Leibniz algebras,J

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Induced structures of averaging commutative and cocommutative infinitesimal bialgebras via a new splitting of perm algebras Unresolved cited work

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Induced structures of averaging commutative and cocommutative infinitesimal bialgebras via a new splitting of perm algebras Unresolved cited work

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Observation df9578ed-ccbb-4d86-a980-b190083b4968 · outbound

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Induced structures of averaging commutative and cocommutative infinitesimal bialgebras via a new splitting of perm algebras Liu and C

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Observation e7c7cf17-817a-4190-ae3a-c9811a5b8384 · outbound

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Induced structures of averaging commutative and cocommutative infinitesimal bialgebras via a new splitting of perm algebras Liu and C

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Observation 9f72654b-2ac3-4c8c-8516-aea09a4a51de · outbound

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Induced structures of averaging commutative and cocommutative infinitesimal bialgebras via a new splitting of perm algebras Loday and B

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Induced structures of averaging commutative and cocommutative infinitesimal bialgebras via a new splitting of perm algebras Unresolved cited work

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Observation 6a33a747-396e-4d8e-90f4-28c6e231fa1a · outbound

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Induced structures of averaging commutative and cocommutative infinitesimal bialgebras via a new splitting of perm algebras Ni and C

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Observation a82a30a3-dc24-437d-be6a-db1fb95eb396 · outbound

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Induced structures of averaging commutative and cocommutative infinitesimal bialgebras via a new splitting of perm algebras Ni and C

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Observation 4dcc6cad-e2f7-4e7a-aedb-c38646312598 · outbound

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Induced structures of averaging commutative and cocommutative infinitesimal bialgebras via a new splitting of perm algebras Nicolai and H

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Observation 791fc5ca-dbae-4b51-8307-5eb93e48d37c · outbound

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Induced structures of averaging commutative and cocommutative infinitesimal bialgebras via a new splitting of perm algebras Symmetries and Groups in Contemporary Physics

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Observation 2c2b47ea-ad4f-4de2-8009-d471bb2a12d8 · outbound

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Induced structures of averaging commutative and cocommutative infinitesimal bialgebras via a new splitting of perm algebras Unresolved cited work

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Induced structures of averaging commutative and cocommutative infinitesimal bialgebras via a new splitting of perm algebras Pei and L

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Induced structures of averaging commutative and cocommutative infinitesimal bialgebras via a new splitting of perm algebras Reynolds, On the dynamic theory of incompressible viscous fluids,Phil

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Observation 5f7d396c-47c2-4577-9216-9397c7dee0e3 · outbound

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Induced structures of averaging commutative and cocommutative infinitesimal bialgebras via a new splitting of perm algebras Rota, Reynolds operators,Proc

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This paper cites Sheng, R.

Induced structures of averaging commutative and cocommutative infinitesimal bialgebras via a new splitting of perm algebras Sheng, R

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Observation 2e3cc3aa-4349-4b5e-80b2-0e501d9b4c72 · outbound

This paper cites Tang and Y.

Induced structures of averaging commutative and cocommutative infinitesimal bialgebras via a new splitting of perm algebras Tang and Y

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Observation 1fa47ff7-2362-4186-a0dc-13593042d608 · outbound

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Induced structures of averaging commutative and cocommutative infinitesimal bialgebras via a new splitting of perm algebras Cohomology theory of averaging algebras, $L_\infty$-structures and homotopy averaging algebras

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Observation 496674f1-4f13-4930-8060-7ba2feb3afc9 · outbound

This paper cites Averaging operators on groups and Hopf algebras.

Induced structures of averaging commutative and cocommutative infinitesimal bialgebras via a new splitting of perm algebras Averaging operators on groups and Hopf algebras

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Induced structures of averaging commutative and cocommutative infinitesimal bialgebras via a new splitting of perm algebras Zusmanovich, Invariants of Lie algebras extended over commutative algebras without unit,J

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Bialgebra theory, the Yang-Baxter equation and relative Rota-Baxter operators for diassociative algebras cites this paper.

Bialgebra theory, the Yang-Baxter equation and relative Rota-Baxter operators for diassociative algebras Induced structures of averaging commutative and cocommutative infinitesimal bialgebras via a new splitting of perm algebras

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