Parallelepipeds, nilpotent groups and Gowers norms

Bernard Host; Bryna Kra

Bulletin de la Société Mathématique de France (2008)

  • Volume: 136, Issue: 3, page 405-437
  • ISSN: 0037-9484

Abstract

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In his proof of Szemerédi’s Theorem, Gowers introduced certain norms that are defined on a parallelepiped structure. A natural question is on which sets a parallelepiped structure (and thus a Gowers 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.

How to cite

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Host, Bernard, and Kra, Bryna. "Parallelepipeds, nilpotent groups and Gowers norms." Bulletin de la Société Mathématique de France 136.3 (2008): 405-437. <http://eudml.org/doc/272478>.

@article{Host2008,
abstract = {In his proof of Szemerédi’s Theorem, Gowers introduced certain norms that are defined on a parallelepiped structure. A natural question is on which sets a parallelepiped structure (and thus a Gowers 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.},
author = {Host, Bernard, Kra, Bryna},
journal = {Bulletin de la Société Mathématique de France},
keywords = {parallelepiped; nilpotent group; Gowers norms},
language = {eng},
number = {3},
pages = {405-437},
publisher = {Société mathématique de France},
title = {Parallelepipeds, nilpotent groups and Gowers norms},
url = {http://eudml.org/doc/272478},
volume = {136},
year = {2008},
}

TY - JOUR
AU - Host, Bernard
AU - Kra, Bryna
TI - Parallelepipeds, nilpotent groups and Gowers norms
JO - Bulletin de la Société Mathématique de France
PY - 2008
PB - Société mathématique de France
VL - 136
IS - 3
SP - 405
EP - 437
AB - In his proof of Szemerédi’s Theorem, Gowers introduced certain norms that are defined on a parallelepiped structure. A natural question is on which sets a parallelepiped structure (and thus a Gowers 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.
LA - eng
KW - parallelepiped; nilpotent group; Gowers norms
UR - http://eudml.org/doc/272478
ER -

References

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  12. [12] M. Lazard – « Sur les groupes nilpotents et les anneaux de Lie », Ann. Sci. Ecole Norm. Sup. (3) 71 (1954), p. 101–190. Zbl0055.25103MR88496
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  14. [14] —, « Polynomial mappings of groups », Israel J. Math.129 (2002), p. 29–60. Zbl1007.20035MR1910931
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