Algebraic Anosov actions of nilpotent Lie groups

In this paper we classify algebraic Anosov actions of nilpotent Lie groups on closed manifolds, extending the previous results by P. Tomter (1970, 1975) [17,18]. 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.