Algebraic Anosov actions of Nilpotent Lie groups

TL;DR

This paper classifies algebraic Anosov actions of nilpotent Lie groups on closed manifolds, revealing they are all related to suspensions of Z^k actions or Weyl chamber actions, and explores their connection to Cartan subalgebras.

Contribution

It extends previous classifications by showing all algebraic Anosov actions of nilpotent Lie groups are nil-suspensions over known types and relates them to Cartan subalgebras.

Findings

All algebraic Anosov actions are nil-suspensions over Z^k actions or Weyl chamber actions.

The generalized Verjovsky conjecture holds in this algebraic setting.

A connection between algebraic Anosov actions and Cartan subalgebras is established.

Abstract

In this paper we classify algebraic Anosov actions of nilpotent Lie groups on closed manifolds, extending the previous results by P. Tomter. We show that they are all nil-suspensions over either suspensions of Anosov actions of Z^k on nilmanifolds, or (modified) Weyl chamber actions. We check the validity of the generalized Verjovsky conjecture in this algebraic context. We also point out an intimate relation between algebraic Anosov actions and Cartan subalgebras in general real Lie groups.