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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 Serie 9 16 (2005), fasc. n.4, p. 265-270, (English)
pdf (892 Kb), djvu (338 Kb). | MR2255009 | Zbl 1114.22008

Sunto

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.
Referenze Bibliografiche
[1] L. AUSLANDER, Lecture notes on nil-theta functions. CBMS Reg. Conf. Series Math., 34, Amer. Math. Soc., Providence 1977. | MR 466409 | Zbl 0421.22001
[2] P. BARBANO, Automorphisms and quasiconformal mappings of Heisenberg type groups. J. of Lie Theory, vol. 8, 1998, 255-277. | fulltext EuDML | MR 1650337 | Zbl 0906.22007
[3] A. BOREL, Introduction aux Groups Arithmetiques. Hermann, Paris 1969. | MR 244260 | Zbl 0186.33202
[4] A. BOREL - HARISH-CHANDRA, Arithmetic subgroups of algebraic groups. Annals of Math., 75, 1962, 485-535. | MR 147566 | Zbl 0107.14804
[5] C. CHABAUTY, Limites d'ensembles et géométrie des nombres. Bull. Soc. Math. de France, 78, 1950, 143-151. | fulltext EuDML | fulltext mini-dml | MR 38983 | Zbl 0039.04101
[6] G. CRANDALL - J. DODZIUK, Integral Structures on $H$-type Lie Algebras. J. of Lie Theory, 12, 2002, 69-79. | fulltext EuDML | fulltext mini-dml | MR 1885037 | Zbl 1035.17018
[7] G.P. HOCHSCHILD, The Structure of Lie Groups. Holden Day, San Francisco 1965. | MR 207883 | Zbl 0131.02702
[8] K. MAHLER, 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] A. MALCEV, On a class of homogeneous spaces. Amer. Math. Soc. Translation Series, 39, 1951. | MR 39734 | Zbl 0034.01701
[10] G. MARGULIS, 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] C. MOORE, Decompositions of Unitary Representations defined by Discrete subgroups of Nilpotent Groups. Annals of Math., 82, 1965. | MR 181701 | Zbl 0139.30702
[12] R. MOSAK - M. MOSKOWITZ, Zariski density in Lie groups. Israel J. Math., 52, 1985, 1-14. | fulltext (doi) | MR 815596 | Zbl 0585.22009
[13] R. MOSAK - M. MOSKOWITZ, Stabilizers of lattices in Lie groups. J. of Lie Theory, vol. 4, 1994, 1-16. | fulltext EuDML | MR 1326948 | Zbl 0823.22012
[14] M. MOSKOWITZ, Some Remarks on Automorphisms of Bounded Displacement and Bounded Cocycles. Monatshefte für Math., 85, 1978, 323-336. | fulltext EuDML | fulltext (doi) | MR 510628 | Zbl 0391.22004
[15] H. WHITNEY, Elementary structure of real algebraic varieties. Ann. of Math., 66, 1957, 545-556. | MR 95844 | Zbl 0078.13403

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