Theoretical analysis establishes cohomology for Reynolds Lie triple systems, showing that degree-three and degree-five cocycles govern deformations, extensions, and higher-order 2-systems.
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.
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Mu et al. (2026) studied this question.
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