CIEM   05476
CENTRO DE INVESTIGACION Y ESTUDIOS DE MATEMATICA
Unidad Ejecutora - UE
artículos
Título:
On Anosov automorphisms of nilmanifolds
Autor/es:
JORGE LAURET, CYNTHIA WILL
Revista:
JOURNAL OF PURE AND APPLIED ALGEBRA
Editorial:
Elsevier
Referencias:
Año: 2008 vol. 212 p. 1747 - 1755
ISSN:
0022-4049
Resumen:
The only known examples of Anosov diffeomorphisms are hyperbolic
automorphisms of infranilmanifolds, and the existence of such
automorphisms is a really strong condition on the rational nilpotent
Lie algebra determined by the lattice, so called an Anosov Lie
algebra. We prove that $\ngo\oplus...\oplus\ngo$
($s$ times, $s\geq 2$) has an Anosov rational form for any graded real
nilpotent Lie algebra $\ngo$ having a rational form. We also obtain
some obstructions for the types of nilpotent Lie algebras allowed, and
use the fact that the eigenvalues of the automorphism are algebraic
integers (even units) to show that the types $(5,3)$ and $(3,3,2)$ are
not possible for Anosov Lie algebras.