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Westudyactionsbyhigher-rankabeliangroupsonquotientsofse- misimple Lie groups with finite center. First, we consider actions arising from the flows of two commuting elements of the Lie algebra—one nilpotent and the other semisimple. Second, we consider actions arising from two commut- ing unipotentflows that come from an embedded copy of SL(2,R) k ×SL(2,R) l . In both cases we show that any smooth R-valued cocycle over the action is cohomologous to a constant cocycle via a smooth transfer function. These results build on theorems of D. Mieczkowski, where the same is shown for ac- tions on (SL(2,R)×SL(2,R))/Γ.

Cocycles over higher-rank abelian actions on quotients of semisimple Lie groups