Skip to content
DraconiticResearch
Search Sources API
194,164 studies31 sourcesUpdated 41 min ago
PreprintCC BY 4.0arXiv

Classification of three-dimensional Leibniz dialgebras with two-dimensional annihilator

  • Naurizbay Uzakbaev
Open at sourcePDFDOICite

Abstract

A Leibniz dialgebra is a vector space with two bilinear products dashv and ⊒ satisfying the dialgebra analogue of the right Leibniz identity. This notion is obtained by the same standard procedure that turns the associative identity into the axioms of Loday's associative dialgebras. In particular, (π’Ÿβ„’,dashv) is a right Leibniz algebra, so a Leibniz dialgebra is a Leibniz algebra together with a second, compatible product. This paper recalls the definition of Leibniz dialgebras and continue the algebraic classification of three-dimensional complex Leibniz dialgebras. This paper describes up to isomorphism all Leibniz dialgebras (π’Ÿβ„’,dashv,⊒) for which the Leibniz algebra (π’Ÿβ„’,dashv) is isomorphic to one of the algebras β„’8(Ξ±), β„’9, β„’10, β„’11 of the classification of three-dimensional complex Leibniz algebras. The result consists 18 families of pairwise non-isomorphic Leibniz dialgebras, nine of which depend on a complex parameter.

Related

  1. Derivation Algebras of Three-Dimensional Leibniz Algebras: A Complete Description
    Leonid A. Kurdachenko, Oleksandr O. Pypka, Mykola M. Semko
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  2. Automorphism Groups of Three-Dimensional Leibniz Algebras: A Complete Description
    Leonid A. Kurdachenko, Oleksandr O. Pypka, Mykola M. Semko
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  3. Classification of all non-split central extensions of naturally graded 2-filiform non-Lie Leibniz algebras
    Kobiljon Abdurasulov, Jobir Adashev
    arXivPreprintCC BY-SA 4.0Full textAlgebra & number theoryarXiv
  4. Isomorphism classes and geometric classification of three-dimensional Jordan algebras and the length function
    Isabel Hernandez, Maria Eugenia Martin, Rodrigo Lucas Rodrigues +1
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  5. Classification of Nijenhuis operators on three-dimensional multiplicative simple Bihom-Lie algebras
    Bouzid Mosbahi
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv

Cite

BibTeXRIS
BibTeX
@misc{uzakbaev2026classification,
  title = {{Classification of three-dimensional Leibniz dialgebras with two-dimensional annihilator}},
  author = {Naurizbay Uzakbaev},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.00109},
  eprint = {2611.00109},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.00109},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Classification of three-dimensional Leibniz dialgebras with two-dimensional annihilator
AU  - Naurizbay Uzakbaev
PY  - 2026
DA  - 2026/11/01
PB  - arXiv
DO  - 10.48550/arxiv.2611.00109
UR  - https://arxiv.org/abs/2611.00109
AB  - A Leibniz dialgebra is a vector space with two bilinear products dashv and ⊒ satisfying the dialgebra analogue of the right Leibniz identity. This notion is obtained by the same standard procedure that turns the associative identity into the axioms of Loday's associative dialgebras. In particular, (π’Ÿβ„’,dashv) is a right Leibniz algebra, so a Leibniz dialgebra is a Leibniz algebra together with a second, compatible product. This paper recalls the definition of Leibniz dialgebras and continue the algebraic classification of three-dimensional complex Leibniz dialgebras. This paper describes up to isomorphism all Leibniz dialgebras (π’Ÿβ„’,dashv,⊒) for which the Leibniz algebra (π’Ÿβ„’,dashv) is isomorphic to one of the algebras β„’_8(Ξ±), β„’_9, β„’_10, β„’_11 of the classification of three-dimensional complex Leibniz algebras. The result consists 18 families of pairwise non-isomorphic Leibniz dialgebras, nine of which depend on a complex parameter.
ER  -