Geodesic
Integral Structures on H-type Lie Algebras
Journal of Lie theory, Tome 12 (2002) no. 1, pp. 69-79 Cet article a éte moissonné depuis la source Heldermann Verlag

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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},
     year = {2002},
     volume = {12},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JLT_2002_12_1_JLT_2002_12_1_a4/}
}
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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/