Cohomologies and deformations of O-operators on Lie triple systems
Taoufik Chtioui, Atef Hajjaji, Sami Mabrouk, Abdenacer Makhlouf
Source abstract
In this paper, first, we provide a graded Lie algebra whose Maurer–Cartan elements characterize Lie triple system structures. Then, we use it to study cohomology and deformations of O-operators on Lie triple systems by constructing a Lie 3-algebra whose Maurer–Cartan elements are O-operators. Furthermore, we define a cohomology of an O-operator T as the Lie–Yamaguti cohomology of a certain Lie triple system induced by T with coefficients in a suitable representation. Therefore, we consider infinitesimal and formal deformations of O-operators from a cohomological viewpoint. Moreover, we provide relationships between O-operators on Lie algebras and associated Lie triple systems.
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