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PreprintCC0arXiv

Local (Anti-)Superderivations on Nilpotent Lie Superalgebras

  • Xiaohui Chi
  • Huiyi Zhang
  • Lingxin Meng
  • Liming Tang
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Abstract

In this paper, we study local superderivations and local anti-superderivations of finite-dimensional nilpotent Lie superalgebras over a field 𝔽 with char𝔽≠2. First, we prove that every finite-dimensional two-step nilpotent Lie superalgebra admits pure local superderivations and pure local anti-superderivations (namely, local (anti-)superderivations that are not (anti-)superderivations). For nilpotent Lie superalgebras of nilpotency index greater than two, we establish sufficient conditions for the existence of pure local superderivations and pure local anti-superderivations. In particular, we prove that every three-step nilpotent Lie superalgebra admits a pure local superderivation.

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Cite

BibTeXRIS
BibTeX
@misc{chi2026local,
  title = {{Local (Anti-)Superderivations on Nilpotent Lie Superalgebras}},
  author = {Xiaohui Chi and Huiyi Zhang and Lingxin Meng and Liming Tang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2607.00393},
  eprint = {2607.00393},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.00393},
  note = {CC0},
}
RIS
TY  - UNPB
TI  - Local (Anti-)Superderivations on Nilpotent Lie Superalgebras
AU  - Xiaohui Chi
AU  - Huiyi Zhang
AU  - Lingxin Meng
AU  - Liming Tang
PY  - 2026
DA  - 2026/10/08
PB  - arXiv
DO  - 10.48550/arxiv.2607.00393
UR  - https://arxiv.org/abs/2607.00393
AB  - In this paper, we study local superderivations and local anti-superderivations of finite-dimensional nilpotent Lie superalgebras over a field 𝔽 with char𝔽≠2. First, we prove that every finite-dimensional two-step nilpotent Lie superalgebra admits pure local superderivations and pure local anti-superderivations (namely, local (anti-)superderivations that are not (anti-)superderivations). For nilpotent Lie superalgebras of nilpotency index greater than two, we establish sufficient conditions for the existence of pure local superderivations and pure local anti-superderivations. In particular, we prove that every three-step nilpotent Lie superalgebra admits a pure local superderivation.
ER  -