Anosov Lie algebras and algebraic units in number fields

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

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: (1) Every 7-dimensional Anosov nilmanifold is toral, and (2) every 8-dimensional Anosov Lie algebra with 3 or 5-dimensional derived algebra contains an abelian factor.

Original languageEnglish
Pages (from-to)79-90
Number of pages12
JournalMonatshefte fur Mathematik
Volume165
Issue number1
DOIs
StatePublished - Jan 2012

Keywords

  • Anosov diffeomorphisms
  • Hyperbolic automorphisms
  • Nilmanifolds
  • Nilpotent Lie algebras

Fingerprint

Dive into the research topics of 'Anosov Lie algebras and algebraic units in number fields'. Together they form a unique fingerprint.

Cite this