Cocycle superrigidity for ergodic actions of non-semisimple Lie groups

1996/07/01 by Witte, Dave
#Dynamical Systems (math.DS) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.math/9607219

Abstract

Suppose L is a semisimple Levi subgroup of a connected Lie group~G, X is a Borel G-space with finite invariant measure, and α\colon X × G → \GL_n(\real) is a Borel cocycle. Assume L has finite center, and that the real rank of every simple factor of~L is at least two. We show that if L is ergodic on~X, and the restriction of~α to~X × L is cohomologous to a homomorphism (modulo a compact group), then, after passing to a finite cover of~X, the cocycle α itself is cohomologous to a homomorphism (modulo a compact group).

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