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arXiv · 2609.21703

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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Jon Beristain, Abdenacer Makhlouf. 2026-09-18. Restricted (Relative) Rota-Baxter operators on restricted Lie algebras and restricted Lie triple systems and related structures. https://arxiv.org/abs/2609.21703

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