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Local rigidity of partially hyperbolic actions

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  • We prove the local differentiable rigidity of partially hyperbolic abelian algebraic high-rank actions on compact homogeneous spaces obtained from simple indefinite orthogonal and unitary groups. The conclusions are based on geometric Katok-Damjanovic way and progress towards computations of the Schur multipliers of these non-split groups.
    Mathematics Subject Classification: 37C85.

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  • [1]

    M. Brin, Y. Pesin, Partially hyperbolic dynamical systems, (Russian) Izv. Akad. Nauk SSSR Ser. Mat., 38 (1974), 170-212.

    [2]

    D. Damjanovic and A. Katok, Periodic cycle functionals and Cocycle rigidity for certain partially hyperbolic $\RR^k$ actions, Discr. Cont. Dyn.Syst., 13 (2005), 985-1005.

    [3]

    D. Damjanovic and A. KatokLocal rigidity of partially hyperbolic actions. II. The geometric method and restrictions of Weyl Chamber flows on $SL(n,\RR)/\Gamma$, http://www.math.psu.edu/katok_a/papers.html.

    [4]

    D. Damjanovic and A. Katok, Local rigidity of partially hyperbolic actions. I. KAM method and $\ZZ^k$ actions on the torus, Annals of Math, 2010, to appear.

    [5]

    D. Damjanovic, Central extensions of simple Lie groups and rigidity of some abelian partially hyperbolic algebraic actions, J. Modern Dyn., 1 (2007), 665-688.

    [6]

    Vinay V. Deodhar, On central extensions of rational points of algebraic groups, Amer. J. Math., 100 (1978), 303-386.doi: doi:10.2307/2373853.

    [7]

    A. J. Hahn and O. T. O'Meara, The classical groups and K-theory, Springer Verlag, Berlin, 1980, 55-58.

    [8]

    M. Hirsch, C. Pugh and M. Shub, "Invariant Manifolds. Lecture Notes in Mathematics," 583, Springer Verlag, Berlin, 1977.

    [9]

    A. Katok and R. Spatzier, Differential rigidity of Anosov actions of higher rank abelian groups and algebraic lattice actions, Proc. Steklov Inst. Math., 216 (1997), 287-314.

    [10]

    G. A. Margulis, "Discrete Subgroups of Semisimple Lie Groups," Springer-Verlag, 1991.

    [11]

    G. A. Margulis and N. Qian, Rigidity of weakly hyperbolic actions of higher real rank semisimple Lie groups and their lattices, Ergodic Theory Dynam. Systems, 21 (2001), 121-164.doi: doi:10.1017/S0143385701001109.

    [12]

    R. Steinberg, Generateurs, relations et revetements de groupes algebriques, Colloque de Bruxelles, 1962, 113-127.

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