Geodesic
Integral Structures on H-type Lie Algebras
Journal of Lie theory, Tome 12 (2002) no. 1, pp. 69-79.

Voir la notice de l'article provenant de la source Heldermann Verlag

We prove that every H-type Lie algebra possesses a basis with respect to which the structure constants are integers. Existence of such an integral basis implies via the Mal'cev criterion that all simply connected H-type Lie groups contain co-compact lattices. Since the Campbell-Hausdorff formula is very simple for two-step nilpotent Lie groups we can actually avoid invoking the Mal'cev criterion and exhibit our lattices in an explicit way. As an application, we calculate the isoperimetric dimensions of H-type groups. 
@article{JLT_2002_12_1_JLT_2002_12_1_a4,
     author = {G. Crandall and J. Dodziuk },
     title = {Integral {Structures} on {H-type} {Lie} {Algebras}},
     journal = {Journal of Lie theory},
     pages = {69--79},
     publisher = {mathdoc},
     volume = {12},
     number = {1},
     year = {2002},
     url = {http://geodesic.mathdoc.fr/item/JLT_2002_12_1_JLT_2002_12_1_a4/}
}
TY  - JOUR
AU  - G. Crandall
AU  - J. Dodziuk 
TI  - Integral Structures on H-type Lie Algebras
JO  - Journal of Lie theory
PY  - 2002
SP  - 69
EP  - 79
VL  - 12
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JLT_2002_12_1_JLT_2002_12_1_a4/
ID  - JLT_2002_12_1_JLT_2002_12_1_a4
ER  - 
%0 Journal Article
%A G. Crandall
%A J. Dodziuk 
%T Integral Structures on H-type Lie Algebras
%J Journal of Lie theory
%D 2002
%P 69-79
%V 12
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JLT_2002_12_1_JLT_2002_12_1_a4/
%F JLT_2002_12_1_JLT_2002_12_1_a4
G. Crandall; J. Dodziuk . Integral Structures on H-type Lie Algebras. Journal of Lie theory, Tome 12 (2002) no. 1, pp. 69-79. http://geodesic.mathdoc.fr/item/JLT_2002_12_1_JLT_2002_12_1_a4/