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arXiv · 1706.05647

Ergodicity of algebraic actions of nilpotent groups

Siddhartha Bhattacharya
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Abstract

An algebraic $\Gamma$-action is an action of a countable group $\Gamma$ on a compact abelian group $X$ by continuous automorphisms of $X$. We prove that any expansive algebraic action of a finitely generated nilpotent group $\Gamma$ 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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Siddhartha Bhattacharya. 2017-06-18. Ergodicity of algebraic actions of nilpotent groups. https://arxiv.org/abs/1706.05647

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