## Abstract

The classification of all real and rational Anosov Lie algebras up to dimension 8 is given by Lauret and Will. In this paper we study 9-dimensional Anosov Lie algebras by using the properties of very special algebraic numbers and Lie algebra classification tools. We prove that there exists a unique, up to isomorphism, complex 3-step Anosov Lie algebra of dimension 9. In the 2-step case, we prove that a 2-step 9-dimensional Anosov Lie algebra with no abelian factor must have a 3-dimensional derived algebra and we characterize these Lie algebras in terms of their Pfaffian forms. Among these Lie algebras, we exhibit a family of infinitely many complex non-isomorphic Anosov Lie algebras.

Original language | English |
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Pages (from-to) | 857-873 |

Number of pages | 17 |

Journal | Journal of Lie Theory |

Volume | 25 |

Issue number | 3 |

State | Published - 2015 |

## Keywords

- Anosov Lie algebras
- Hyperbolic automorphisms
- Nilmanifolds
- Nilpotent lie algebras