Skip to content
DraconiticResearch
Search Sources API
203,203 studies31 sourcesUpdated 28 min ago
PreprintCC0arXiv

Generalized Mock-Poisson Algebras: Constructions and Structural Properties

  • Zafar Normatov
Open at sourcePDFDOICite

Abstract

In this paper, we introduce generalized mock-Poisson algebras as a mock analogue of generalized Poisson algebras. We prove that A∗3 is an ideal annihilated by both operations and that the quotient A/A∗3 is a mock-Poisson algebra. We also show that the dimension seven is the smallest dimension in which a generalized mock-Poisson algebra need not be a mock-Poisson algebra. We give several constructions using derivations, anti-Zinbiel algebras, tensor products, and one-dimensional extensions. We study polarization and depolarization and characterize the corresponding admissible algebras. We prove that every finite-dimensional generalized mock-Poisson algebra over a field of characteristic zero is nilpotent. Finally, we describe representations in terms of semidirect products.

Related

  1. δ-Mock-Novikov Algebras: Structural Theory, Operad and Poisson-Type Constructions
    Jie Ruan, Zafar Normatov
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  2. Poisson n-Lie algebras: constructions and the structure of solvable algebras
    Xinru Cao, Zafar Normatov, Bakhrom Omirov
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  3. Commutativity Criteria and Structural Properties of Prime Near-Rings Admitting Right Generalized Derivations on Specific Ideals
    Khaled Aldwoah, Inzamam ul Huque, Hafedh Alnoghashi +3
    AxiomsPeer-reviewedCC BY 4.0Algebra & number theoryCrossref
  4. Discrete differential-geometric Poisson brackets: general theory and explicit constructions
    Marta Dell'Atti, Giorgio Gubbiotti, Pierandrea Vergallo
    arXivPreprintarXiv licenceFull textAlgebra & number theoryMathematical physicsarXiv
  5. RELATIVE BIHOM-PRE-ANTI-FLEXIBLE ALGEBRAS : CONSTRUCTIONS AND RELATED ALGEBRAIC STRUCTURES
    Aloulou Walid, Jebli Mansour
    HALPreprintPublisher termsFull textAlgebra & number theoryHAL

Cite

BibTeXRIS
BibTeX
@misc{normatov2026generalized,
  title = {{Generalized Mock-Poisson Algebras: Constructions and Structural Properties}},
  author = {Zafar Normatov},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.23143},
  eprint = {2610.23143},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.23143},
  note = {CC0},
}
RIS
TY  - UNPB
TI  - Generalized Mock-Poisson Algebras: Constructions and Structural Properties
AU  - Zafar Normatov
PY  - 2026
DA  - 2026/10/16
PB  - arXiv
DO  - 10.48550/arxiv.2610.23143
UR  - https://arxiv.org/abs/2610.23143
AB  - In this paper, we introduce generalized mock-Poisson algebras as a mock analogue of generalized Poisson algebras. We prove that A_∗^3 is an ideal annihilated by both operations and that the quotient A/A_∗^3 is a mock-Poisson algebra. We also show that the dimension seven is the smallest dimension in which a generalized mock-Poisson algebra need not be a mock-Poisson algebra. We give several constructions using derivations, anti-Zinbiel algebras, tensor products, and one-dimensional extensions. We study polarization and depolarization and characterize the corresponding admissible algebras. We prove that every finite-dimensional generalized mock-Poisson algebra over a field of characteristic zero is nilpotent. Finally, we describe representations in terms of semidirect products.
ER  -