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arXiv · 2310.13728

Weighted $\mathcal{O}$-operators on Hom-Lie triple systems

Wen Teng·Jiulin Jin
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Abstract

In this paper, we first introduce the notion of a weighted $\mathcal{O}$-operator on Hom-Lie triple systems with respect to an action on another Hom-Lie triple system. Next, we construct a cohomology of weighted $\mathcal{O}$-operator on Hom-Lie triple systems, we use the first cohomology group to classify linear deformations and we investigate the obstruction class of an extendable $n$-order deformation. We end this paper by introducing a new algebraic structure, in connection with weighted $\mathcal{O}$-operators, called Hom-post-Lie triple system. We further show that Hom-post-Lie triple systems can be derived from Hom-post-Lie algebras.

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Wen Teng, Jiulin Jin. 2023-10-21. Weighted $\mathcal{O}$-operators on Hom-Lie triple systems. https://doi.org/10.1007/s11785-026-01908-6

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