  We prove that one can obtain natural bundles of Lie algebras on rank two
s-K\"ahler manifolds, whose fibres are isomorphic to so(s+1,s+1), su(s+1,s+1)
and sl(2s + 2,\R). In the most rigid case (which includes complex tori and
abelian varieties) these bundles have natural flat connections, whose flat
global sections act naturally on cohomology. We also present several natural
examples of manifolds which can be equipped with an s-K\"ahler structure with
various levels of rigidity: complex tori and abelian varieties, cotangent
bundles of smooth manifolds and moduli of pointed elliptic curves.

Algebraic Geometry;Differential Geometry