2023/09/04 by R. Gharbi, Gharbi, Rahma, Sami Mabrouk +3
Mathematics · Medicine · #Geometric Analysis and Curvature Flows #Advanced Neuroimaging Techniques and Applications #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.2309.01385
The purpose of this paper is to introduce and study the notion of generalized Reynolds operators on Lie triple systems with representations (Abbr. \textsfL.t.sRep pairs) as generalization of weighted Reynolds operators on Lie triple systems. First, We construct an L∞-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.