
Journal of Lie Theory 12 (2002), No. 1, 069079 Copyright Heldermann Verlag 2002 Integral Structures on Htype Lie Algebras Gordon Crandall Dept. of Mathematics, LaGuardia Community College, City University of New York, 3110 Thomson Avenue, Long Island City, NY 11101, U.S.A. Józef Dodziuk Graduate Center, City University, 365 Fifth Avenue, New York, NY 10016, U.S.A. We prove that every Htype 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 Htype Lie groups contain cocompact lattices. Since the CampbellHausdorff formula is very simple for twostep 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 Htype groups. [ Fulltextpdf (179 KB)] 