PARALLELEPIPEDS, NILPOTENT GROUPS AND GOWERS NORMS

Bernard Host (1) , Bryna Kra

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

In his proof of Szemeredi's Theorem, Cowers introduced certain norms that are defined on a parallelepiped structure. A natural question is on which sets a parallelepiped structure (and thus a Cowers norm) can be defined. We focus on dimensions 2 and 3 and show when this possible, and describe a correspondence between the parallelepiped structures and nilpotent groups.

Domaines: Physique mathématique [math-ph]

Bernard Host, Bryna Kra. PARALLELEPIPEDS, NILPOTENT GROUPS AND GOWERS NORMS. Bulletin de la société mathématique de France, 2008, 136 (3), pp.405--437. ⟨hal-00693082⟩