Journal of Lie Theory

no. 1
Integral Structures on H-type Lie Algebras
Journal of Lie Theory, Volume 12 (2002) no. 1, pp. 69-79
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.
DOI: 10.5802/jolt.253
Classification: 17B30, 22E25
Keywords: H-type Lie algebra, H-type group, integral structures 
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     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},
     doi = {10.5802/jolt.253},
     zbl = {1035.17018},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.253/}
}
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G. Crandall; J. Dodziuk. Integral Structures on H-type Lie Algebras. Journal of Lie Theory, Volume 12 (2002) no. 1, pp. 69-79. doi: 10.5802/jolt.253

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