Tracy L. Payne
Abstract
Each matrix $A$ in $GL_n(Z)$naturally defines an automorphism $f$ of the free $r$-step nilpotentLie algebra $\frf_{n,r}$. We study the relationship between thematrix $A$ and the eigenvalues and rational invariant subspaces for$f$. We give applications to the study of Anosov automorphisms.
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Each matrix $A$ in $GL_n(Z)$naturally defines an automorphism $f$ of the free $r$-step nilpotentLie algebra $\frf_{n,r}$. We study the relationship between thematrix $A$ and the eigenvalues and rational invariant subspaces for$f$. We give applications to the study of Anosov automorphisms.
Key concepts: Mathematics, Automorphism, Linear subspace, Pure mathematics, Nilpotent, Invariant (physics), Eigenvalues and eigenvectors, Lie algebra