Anosov Lie algebras and algebraic units in number fields
Dynamical Systems
2010-10-29 v4 Differential Geometry
Abstract
We study nilmanifolds admitting Anosov automorphisms by applying elementary properties of algebraic units in number fields to the associated Anosov Lie algebras. We identify obstructions to the existence of Anosov Lie algebras. The case of 13-dimensional Anosov Lie algebras is worked out as an illustration of the technique. Also, we recapture the following known results: (i) Every 7-dimensional Anosov nilmanifold is toral, and (ii) every 8-dimensional Anosov Lie algebra with 3 or 5-dimensional derived algebra contains an abelian factor.
Keywords
Cite
@article{arxiv.math/0606384,
title = {Anosov Lie algebras and algebraic units in number fields},
author = {Meera G. Mainkar},
journal= {arXiv preprint arXiv:math/0606384},
year = {2010}
}
Comments
12 pages, few changes and change in proof of proposition 2, to appear in Monatshefte f\"ur Mathematik