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PreprintCC BY 4.0arXiv

Restricted (Relative) Rota-Baxter operators on restricted Lie algebras and restricted Lie triple systems and related structures

  • Jon Beristain
  • Abdenacer Makhlouf
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Abstract

The main purpose of this paper is to define and study the notion of restricted Rota-Baxter operator on restricted Lie algebras and restricted Lie triple systems. We provide the relevant properties and the usual connections with pre-Lie structures. We show that the operad of pre-Lie triple systems is the splitting of the operad of Lie triple systems. Moreover, we prove that Jacobson identities hold in pre-Lie triple systems in positive characteristic and then introduce the notion of restricted pre-Lie triple system.

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Cite

BibTeXRIS
BibTeX
@misc{beristain2026restricted,
  title = {{Restricted (Relative) Rota-Baxter operators on restricted Lie algebras and restricted Lie triple systems and related structures}},
  author = {Jon Beristain and Abdenacer Makhlouf},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.21703},
  eprint = {2609.21703},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.21703},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Restricted (Relative) Rota-Baxter operators on restricted Lie algebras and restricted Lie triple systems and related structures
AU  - Jon Beristain
AU  - Abdenacer Makhlouf
PY  - 2026
DA  - 2026/09/18
PB  - arXiv
DO  - 10.48550/arxiv.2609.21703
UR  - https://arxiv.org/abs/2609.21703
AB  - The main purpose of this paper is to define and study the notion of restricted Rota-Baxter operator on restricted Lie algebras and restricted Lie triple systems. We provide the relevant properties and the usual connections with pre-Lie structures. We show that the operad of pre-Lie triple systems is the splitting of the operad of Lie triple systems. Moreover, we prove that Jacobson identities hold in pre-Lie triple systems in positive characteristic and then introduce the notion of restricted pre-Lie triple system.
ER  -