Cohomology of Reynolds Lie Triple Systems and Applications

We establish a cohomology theory for Reynolds Lie triple systems by first developing their representation theory and then assembling the corresponding cochains into a suitable complex. This construction is subsequently applied to deformation and extension problems. In particular, infinitesimal formal deformations are described by degree-three cocycles, while equivalence classes of abelian extensions are determined by the associated cohomology classes. We further introduce Reynolds Lie triple 2-systems and show that the skeletal case is governed by degree-five cocycles of Reynolds Lie triple systems.