# American Institute of Mathematical Sciences

October  2007, 1(4): 665-688. doi: 10.3934/jmd.2007.1.665

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

 1 Department of Mathematics, Harvard University, 1 Oxford Street, Cambridge, MA 02138, United States

Received  February 2007 Revised  July 2007 Published  July 2007

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.
Citation: Danijela Damjanović. Central extensions of simple Lie groups and rigidity of some abelian partially hyperbolic algebraic actions. Journal of Modern Dynamics, 2007, 1 (4) : 665-688. doi: 10.3934/jmd.2007.1.665
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