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δ-Mock-Novikov Algebras: Structural Theory, Operad and Poisson-Type Constructions

  • Jie Ruan
  • Zafar Normatov
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Abstract

We introduce δ-mock-Novikov algebras as a parameter-dependent mock analogue of Novikov algebras. For δ=1, the commutator of a mock-Novikov algebra defines a Malcev algebra. Every δ-mock-Novikov algebra satisfying 𝒜2⊆Ann(𝒜) is shown to be differentially special. At the operadic level, the binary quadratic operad governing δ-mock-Novikov algebras is quadratically self-dual but not Koszul. We prove that finite-dimensional δ-mock-Novikov algebras are nilpotent in characteristic zero and classify those of dimension at most four. Finally, we study the associated Poisson-type structures and establish relations and constructions among them via polarization, depolarization, and tensor products.

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Cite

BibTeXRIS
BibTeX
@misc{ruan2026δmocknovikov,
  title = {{$δ$-Mock-Novikov Algebras: Structural Theory, Operad and Poisson-Type Constructions}},
  author = {Jie Ruan and Zafar Normatov},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.06913},
  eprint = {2609.06913},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.06913},
}
RIS
TY  - UNPB
TI  - δ-Mock-Novikov Algebras: Structural Theory, Operad and Poisson-Type Constructions
AU  - Jie Ruan
AU  - Zafar Normatov
PY  - 2026
DA  - 2026/09/07
PB  - arXiv
DO  - 10.48550/arxiv.2609.06913
UR  - https://arxiv.org/abs/2609.06913
AB  - We introduce δ-mock-Novikov algebras as a parameter-dependent mock analogue of Novikov algebras. For δ=1, the commutator of a mock-Novikov algebra defines a Malcev algebra. Every δ-mock-Novikov algebra satisfying 𝒜^2⊆Ann(𝒜) is shown to be differentially special. At the operadic level, the binary quadratic operad governing δ-mock-Novikov algebras is quadratically self-dual but not Koszul. We prove that finite-dimensional δ-mock-Novikov algebras are nilpotent in characteristic zero and classify those of dimension at most four. Finally, we study the associated Poisson-type structures and establish relations and constructions among them via polarization, depolarization, and tensor products.
ER  -