Anosov automorphisms on nilmanifolds in dimensions 9 and 10

TL;DR

This paper classifies and constructs 9 and 10-dimensional Anosov Lie algebras, revealing new examples and non-existence results using properties of algebraic numbers, advancing understanding of Anosov automorphisms on nilmanifolds.

Contribution

It provides a classification of k-step complex Anosov Lie algebras for dimensions 9 and 10, including explicit examples and non-existence results for certain types.

Findings

Classified k-step complex Anosov Lie algebras for dimensions 9 and 10.

Constructed examples for each type in the 2-step case.

Proved non-existence results for some algebra types.

Abstract

We study 9 and 10-dimensional Anosov Lie algebras, by using the properties of very special algebraic numbers. We classify k-step complex Anosov Lie algebras for $k>2$ and in the two step case, we give an example in each possible type, or we give a non-existence result.