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# Central extensions of simple Lie groups and rigidity of some abelian partially hyperbolic algebraic actions

• We consider partially hyperbolic abelian algebraic higher-rank actions on compact homogeneous spaces obtained from simple split Lie groups of nonsymplectic type. We show that smooth, real-valued cocycles trivialize as well as small cocycles taking values in groups of diffeomorphisms of compact manifolds and some semisimple Lie groups. In the second part of the paper, we show local differentiable rigidity for such actions.
Mathematics Subject Classification: Primary: 37D30, 37D40.

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