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

Danijela Damjanović

doi:10.3934/jmd.2007.1.665

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2007, Volume 1, Issue 4: 665-688. Doi: 10.3934/jmd.2007.1.665

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

Danijela Damjanović^1,

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

Received: January 31, 2007

Revised: June 30, 2007

Published: June 2007

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Abstract

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.

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Mathematics Subject Classification: Primary: 37D30, 37D40.

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