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arXiv · 2309.01385

Maurer-Cartan type cohomology on generalized Reynolds operators and NS-structures on Lie triple systems

Rahma Gharbi·Sami Mabrouk·Abdenacer Makhlouf
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Abstract

The purpose of this paper is to introduce and study the notion of generalized Reynolds operators on Lie triple systems with representations (Abbr. \textsf{L.t.sRep} pairs) as generalization of weighted Reynolds operators on Lie triple systems. First, We construct an $L_{\infty}$-algebra whose Maurer-Cartan elements are generalized Reynolds operators. This allows us to define a Yamaguti cohomology of a generalized Reynolds operator. This cohomology can be seen as the Yamaguti cohomology of a certain Lie triple system with coefficients in a suitable representation. Next, we study deformations of generalized Reynolds operators from cohomological points of view and we investigate the obstruction class of an extendable deformation of order $n$. We end this paper by introducing a new algebraic structure, in connection with generalized Reynolds operator, called NS-Lie triple system. Moreover, we show that NS-Lie triple systems can be derived from NS-Lie algebras.

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BibTeXRIS

Rahma Gharbi, Sami Mabrouk, Abdenacer Makhlouf. 2023-09-04. Maurer-Cartan type cohomology on generalized Reynolds operators and NS-structures on Lie triple systems. https://arxiv.org/abs/2309.01385

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