# American Institute of Mathematical Sciences

January  2009, 3(1): 121-158. doi: 10.3934/jmd.2009.3.121

## Anosov automorphisms of nilpotent Lie algebras

 1 Department of Mathematics, Idaho State University, Pocatello, ID 83209-8085, United States

Received  September 2008 Published  February 2009

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.
Citation: Tracy L. Payne. Anosov automorphisms of nilpotent Lie algebras. Journal of Modern Dynamics, 2009, 3 (1) : 121-158. doi: 10.3934/jmd.2009.3.121
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