Journal of Modern Dynamics (JMD)

Local rigidity of partially hyperbolic actions

Pages: 271 - 327, Issue 2, April 2010      doi:10.3934/jmd.2010.4.271

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Zhenqi Jenny Wang - Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, United States (email)

Abstract: We consider partially hyperbolic abelian algebraic high-rank actions on compact homogeneous spaces obtained from simple indefinite orthogonal and unitary groups. In the first part of the paper, we show local differentiable rigidity for such actions. The conclusions are based on progress toward computations of the Schur multipliers of these non-split groups, which is the main aim of the second part.

Keywords:  action of higher rank abelian groups, cocycles, rigidity, Steinberg symbols, generators and relations in classical Lie groups.
Mathematics Subject Classification:  Primary: 37D; Secondary: 19C, 22E.

Received: October 2009;      Revised: June 2010;      Available Online: August 2010.