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Given an orientable weakly self-dual manifold X of rank two, we build a geometric realization of the Lie algebra sl(6, C) as a naturally defined algebra L C of endomorphisms of the space of differential forms of X. We provide an explicit description of Serre generators in terms of natural generators of L C. This construction gives a bundle on X which is(More)
We study the general properties of rank two s-Kähler manifolds. We present several natural examples of manifolds which can be equipped with this structure with various levels of rigidity: complex tori and abelian varieties, cotangent bundles of smooth manifolds and moduli of pointed elliptic curves. We show how one can obtain natural bundles of Lie algebras(More)
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