Journal of Modern Dynamics (JMD)

Anosov automorphisms of nilpotent Lie algebras

Pages: 121 - 158, Issue 1, January 2009      doi:10.3934/jmd.2009.3.121

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Tracy L. Payne - Department of Mathematics, Idaho State University, Pocatello, ID 83209-8085, United States (email)

Abstract: Each matrix $A$ in $GL_n(Z)$ naturally defines an automorphism $f$ of the free $r$-step nilpotent Lie algebra $\frf_{n,r}$. We study the relationship between the matrix $A$ and the eigenvalues and rational invariant subspaces for $f$. We give applications to the study of Anosov automorphisms.

Keywords:  Anosov automorphism, Anosov diffeomorphism, Anosov Lie algebra, hyperbolic automorphism, nilmanifold, nilpotent Lie algebra.
Mathematics Subject Classification:  Primary: 22E25, 22D45, 37D20.

Received: September 2008;      Available Online: February 2009.