An extension of Mahler's theorem to simply connected nilpotent groups

Martin Moskowitz

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (2005)

  • Volume: 16, Issue: 4, page 265-270
  • ISSN: 1120-6330

Abstract

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This Note gives an extension of Mahler's theorem on lattices in R n to simply connected nilpotent groups with a Q -structure. From this one gets an application to groups of Heisenberg type and a generalization of Hermite's inequality.

How to cite

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Moskowitz, Martin. "An extension of Mahler's theorem to simply connected nilpotent groups." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 16.4 (2005): 265-270. <http://eudml.org/doc/252431>.

@article{Moskowitz2005,
abstract = {This Note gives an extension of Mahler's theorem on lattices in $\mathbb\{R\}^\{n\}$ to simply connected nilpotent groups with a $Q$-structure. From this one gets an application to groups of Heisenberg type and a generalization of Hermite's inequality.},
author = {Moskowitz, Martin},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {log lattices; subgroups of finite index; fundamental domains; measure preserving automorphisms; equivariant maps},
language = {eng},
month = {12},
number = {4},
pages = {265-270},
publisher = {Accademia Nazionale dei Lincei},
title = {An extension of Mahler's theorem to simply connected nilpotent groups},
url = {http://eudml.org/doc/252431},
volume = {16},
year = {2005},
}

TY - JOUR
AU - Moskowitz, Martin
TI - An extension of Mahler's theorem to simply connected nilpotent groups
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 2005/12//
PB - Accademia Nazionale dei Lincei
VL - 16
IS - 4
SP - 265
EP - 270
AB - This Note gives an extension of Mahler's theorem on lattices in $\mathbb{R}^{n}$ to simply connected nilpotent groups with a $Q$-structure. From this one gets an application to groups of Heisenberg type and a generalization of Hermite's inequality.
LA - eng
KW - log lattices; subgroups of finite index; fundamental domains; measure preserving automorphisms; equivariant maps
UR - http://eudml.org/doc/252431
ER -

References

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  10. MARGULIS, G., Discrete Subgroups of Semisimple Lie Groups. Ergebnisse der Mathematik und ihrer Grenzgebiete (3) 17, Springer-Verlag, Berlin-Heidelberg-New York1990. Zbl0732.22008MR1090825
  11. MOORE, C., Decompositions of Unitary Representations defined by Discrete subgroups of Nilpotent Groups. Annals of Math., 82, 1965. Zbl0139.30702MR181701
  12. MOSAK, R. - MOSKOWITZ, M., Zariski density in Lie groups. Israel J. Math., 52, 1985, 1-14. Zbl0585.22009MR815596DOI10.1007/BF02776074
  13. MOSAK, R. - MOSKOWITZ, M., Stabilizers of lattices in Lie groups. J. of Lie Theory, vol. 4, 1994, 1-16. Zbl0823.22012MR1326948
  14. MOSKOWITZ, M., Some Remarks on Automorphisms of Bounded Displacement and Bounded Cocycles. Monatshefte für Math., 85, 1978, 323-336. Zbl0391.22004MR510628DOI10.1007/BF01305961
  15. WHITNEY, H., Elementary structure of real algebraic varieties. Ann. of Math., 66, 1957, 545-556. Zbl0078.13403MR95844

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