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PreprintCC BY 4.0arXiv

1/2 derivations and biderivations of 3-dimensional nilpotent Lie-Yamaguti algebras

  • Hassan Oubba
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Abstract

In this paper, we investigate 1/2-derivations and their corresponding local and 2-local analogues on three-dimensional nilpotent Lie--Yamaguti algebras over a field 𝔽 of characteristic zero. Utilizing the established classification of these algebras, we explicitly determine their structures of 1/2-derivations and biderivations. Furthermore, we characterize the matrix representations of their local 1/2-derivations. Our findings demonstrate that, for the non-abelian algebras under consideration, the space of local 1/2-derivations is strictly larger than that of ordinary 1/2-derivations. In addition, we construct examples of 2-local 1/2-derivations that fail to be global 1/2-derivations. Finally, a complete characterization of the biderivations for these algebras is provided.

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Cite

BibTeXRIS
BibTeX
@misc{oubba2026derivations,
  title = {{$\frac12$ derivations and biderivations of 3-dimensional nilpotent Lie-Yamaguti algebras}},
  author = {Hassan Oubba},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.24852},
  eprint = {2610.24852},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.24852},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - 1/2 derivations and biderivations of 3-dimensional nilpotent Lie-Yamaguti algebras
AU  - Hassan Oubba
PY  - 2026
DA  - 2026/10/17
PB  - arXiv
DO  - 10.48550/arxiv.2610.24852
UR  - https://arxiv.org/abs/2610.24852
AB  - In this paper, we investigate 1/2-derivations and their corresponding local and 2-local analogues on three-dimensional nilpotent Lie--Yamaguti algebras over a field 𝔽 of characteristic zero. Utilizing the established classification of these algebras, we explicitly determine their structures of 1/2-derivations and biderivations. Furthermore, we characterize the matrix representations of their local 1/2-derivations. Our findings demonstrate that, for the non-abelian algebras under consideration, the space of local 1/2-derivations is strictly larger than that of ordinary 1/2-derivations. In addition, we construct examples of 2-local 1/2-derivations that fail to be global 1/2-derivations. Finally, a complete characterization of the biderivations for these algebras is provided.
ER  -