An extension of Mahler's theorem to simply connected nilpotent groups
Moskowitz, Martin
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 16 (2005), p. 265-270 / Harvested from Biblioteca Digitale Italiana di Matematica

This Note gives an extension of Mahler's theorem on lattices in Rn 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.

Publié le : 2005-12-01
@article{RLIN_2005_9_16_4_265_0,
     author = {Martin Moskowitz},
     title = {An extension of Mahler's theorem to simply connected nilpotent groups},
     journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
     volume = {16},
     year = {2005},
     pages = {265-270},
     zbl = {1114.22008},
     mrnumber = {2255009},
     language = {en},
     url = {http://dml.mathdoc.fr/item/RLIN_2005_9_16_4_265_0}
}
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, Tome 16 (2005) pp. 265-270. http://gdmltest.u-ga.fr/item/RLIN_2005_9_16_4_265_0/

[1] Auslander, L., Lecture notes on nil-theta functions. CBMS Reg. Conf. Series Math., 34, Amer. Math. Soc., Providence1977. | MR 466409 | Zbl 0421.22001

[2] Barbano, P., Automorphisms and quasiconformal mappings of Heisenberg type groups. J. of Lie Theory, vol. 8, 1998, 255-277. | MR 1650337 | Zbl 0906.22007

[3] Borel, A., Introduction aux Groups Arithmetiques. Hermann, Paris1969. | MR 244260 | Zbl 0186.33202

[4] Borel, A. - Harish-Chandra, , Arithmetic subgroups of algebraic groups. Annals of Math., 75, 1962, 485-535. | MR 147566 | Zbl 0107.14804

[5] Chabauty, C., Limites d'ensembles et géométrie des nombres. Bull. Soc. Math. de France, 78, 1950, 143-151. | MR 38983 | Zbl 0039.04101

[6] Crandall, G. - Dodziuk, J., Integral Structures on H-type Lie Algebras. J. of Lie Theory, 12, 2002, 69-79. | MR 1885037 | Zbl 1035.17018

[7] Hochschild, G.P., The Structure of Lie Groups. Holden Day, San Francisco1965. | MR 207883 | Zbl 0131.02702

[8] Mahler, K., On Lattice Points in n-dimensional Star Bodies I, Existence theorems. Proc. Roy. Soc. London A, 187, 1946,151-187. | MR 17753 | Zbl 0060.11710

[9] Malcev, A., On a class of homogeneous spaces. Amer. Math. Soc. Translation Series, 39, 1951. | MR 39734 | Zbl 0034.01701

[10] Margulis, G., Discrete Subgroups of Semisimple Lie Groups. Ergebnisse der Mathematik und ihrer Grenzgebiete (3) 17, Springer-Verlag, Berlin-Heidelberg-New York 1990. | MR 1090825 | Zbl 0732.22008

[11] Moore, C., Decompositions of Unitary Representations defined by Discrete subgroups of Nilpotent Groups. Annals of Math., 82, 1965. | MR 181701 | Zbl 0139.30702

[12] Mosak, R. - Moskowitz, M., Zariski density in Lie groups. Israel J. Math., 52, 1985, 1-14. | MR 815596 | Zbl 0585.22009

[13] Mosak, R. - Moskowitz, M., Stabilizers of lattices in Lie groups. J. of Lie Theory, vol. 4, 1994, 1-16. | MR 1326948 | Zbl 0823.22012

[14] Moskowitz, M., Some Remarks on Automorphisms of Bounded Displacement and Bounded Cocycles. Monatshefte für Math., 85, 1978, 323-336. | MR 510628 | Zbl 0391.22004

[15] Whitney, H., Elementary structure of real algebraic varieties. Ann. of Math., 66, 1957, 545-556. | MR 95844 | Zbl 0078.13403