EMIS ELibM Electronic Journals Journal of Lie Theory
Vol. 12, No. 1, pp. 69--79 (2002)

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Integral Structures on H-type Lie Algebras

Gordon Crandall and Józef Dodziuk

Gordon Crandall
Department of Mathematics
LaGuardia Community College
The City University of New York
31-10 Thomson Avenue
Long Island City, NY 11101

Józef Dodziuk
Ph.D. Program in Mathematics
Graduate Center
The City University of New York
365 Fifth Avenue
New York, NY 10016

Abstract: In this paper 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.

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Electronic fulltext finalized on: 30 Oct 2001. This page was last modified: 9 Nov 2001.

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