Ergodicity of algebraic actions of nilpotent groups

2017/06/18 by Siddhartha Bhattacharya, Bhattacharya, Siddhartha
Mathematics · #Mathematical Dynamics and Fractals #Advanced Algebra and Geometry #Advanced Topology and Set Theory

paper · pdf · doi:10.48550/arxiv.1706.05647

Abstract

An algebraic Γ-action is an action of a countable group Γ on a compact abelian group X by continuous automorphisms of X. We prove that any expansive algebraic action of a finitely generated nilpotent group Γ on a connected group X is ergodic. We also show that this result does not hold for actions of polycyclic groups.

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