On rational forms of nilpotent Lie algebras

JORGE LAURET

MONATSHEFETE FUR MATHEMATIK

Año: 2008 vol. 155 p. 15 - 30

0026-9255

An explicit classification of Anosov Lie algebras of dimension $leq 8$ is given in a paper by C. Will and the author.  After a quite involved work carried out  on the real level, it follows that the only real nilpotent Lie algebras of dimension $leq 8$ (without abelian factors) which admit at least one Anosov rational form are $hg_3oplushg_3$, $g_3$, $ggo$, $hg_3oplushg_5$, $hg$ and $lgo_4opluslgo_4$ (see Table ef{notation}). This is a really short list if we bear in mind that there exist several continuous families and hundreds of isolated examples of $7$ and $8$-dimensional nilpotent Lie algebras. After this, it was crucial to know for each of these Lie algebras, a complete list of all their rational forms up to isomorphism.  This information has been obtained in the present paper  and is part of the classification of nilmanifolds admitting an Anosov diffeomorphism in dimension $leq 8$.