Anosov Automorphisms of Nilpotent Lie Algebras

TL;DR

This paper investigates the connection between matrices in GL_n(Z) and automorphisms of nilpotent Lie algebras, focusing on eigenvalues and invariant subspaces, with applications to Anosov automorphisms.

Contribution

It provides new insights into how matrices determine automorphisms of nilpotent Lie algebras and explores their properties related to Anosov automorphisms.

Findings

Characterization of eigenvalues and invariant subspaces for automorphisms

Relationships between matrix properties and Lie algebra automorphisms

Applications to the theory of Anosov automorphisms

Abstract

Each matrix A in GL_n(Z) naturally defines an automorphism f of the free r-step nilpotent Lie algebra on n generators. 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.