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April  2010, 4(2): 271-327. doi: 10.3934/jmd.2010.4.271

Local rigidity of partially hyperbolic actions

Zhenqi Jenny Wang 1,

1. 

Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, United States

Received  October 2009 Revised  June 2010 Published  August 2010

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: rigidity, cocycles, generators and relations in classical Lie groups., Steinberg symbols, action of higher rank abelian groups.
Mathematics Subject Classification: Primary: 37D; Secondary: 19C, 22.
Citation: Zhenqi Jenny Wang. Local rigidity of partially hyperbolic actions. Journal of Modern Dynamics, 2010, 4 (2) : 271-327. doi: 10.3934/jmd.2010.4.271
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