Examples of Anosov Lie algebras

Meera G. Mainkar; Cynthia E. Will

doi:10.3934/dcds.2007.18.39

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2007, Volume 18, Issue 1: 39-52. Doi: 10.3934/dcds.2007.18.39

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Examples of Anosov Lie algebras

Meera G. Mainkar^1, and
Cynthia E. Will^2,

1.
Department of Mathematics, The University of Western Ontario, London, Ontario N6A 5B7
2.
FaMAF and CIEM, Universidad Nacional de Córdoba, Haya de la Torre s/n, 5000 Córdoba

Received: May 31, 2006

Revised: November 30, 2006

Published: December 2006

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Abstract

We construct new families of examples of (real) Anosov Lie algebras, starting with algebraic units. We also give examples of indecomposable Anosov Lie algebras (not a direct sum of proper Lie ideals) of dimension $13$ and $16$, and we conclude that for every $n \geq 6$ with $n \ne 7$ there exists an indecomposable Anosov Lie algebra of dimension $n$.

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Mathematics Subject Classification: Primary: 37D20; Secondary: 22E25, 20F34.

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