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- Positivity of the top lyapunov exponent for cocycles on semisimple lie groups over hyperbolic basesPublication . Bessa, Mário; Bochi, Jairo; Cambrainha, Michel; Matheus, Carlos; Varandas, Paulo; Xu, DishengA theorem of Viana says that almost all cocycles over any hyperbolic system have nonvanishing Lyapunov exponents. In this note we extend this result to cocycles on any noncompact classical semisimple Lie group.