Cohomology and Deformations of Generalized Reynolds Operators on Leibniz Algebras

We introduce generalized Reynolds operators on Leibniz algebras as a generalization of twisted Poisson structures. We define the cohomology of a generalized Reynolds operator K as the Loday–Pirashvili cohomology of a certain Leibniz algebra induced by K with coefficients in a suitable representation. Then we consider formal deformations of generalized Reynolds operators from cohomological points of view. Finally, we introduce and study NS-Leibniz algebras as the underlying structure of generalized Reynolds operators.