Anosov automorphisms on nilmanifolds in dimensions 9 and 10

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.

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