Journal of Lie Theory Vol. 12, No. 1, pp. 6979 (2002) 

Integral Structures on Htype Lie AlgebrasGordon Crandall and Józef DodziukGordon CrandallDepartment of Mathematics LaGuardia Community College The City University of New York 3110 Thomson Avenue Long Island City, NY 11101 crandallgo@lagcc.cuny.edu, Józef Dodziuk Ph.D. Program in Mathematics Graduate Center The City University of New York 365 Fifth Avenue New York, NY 10016 jdodziuk@gc.cuny.edu Abstract: In this paper 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. Full text of the article:
Electronic fulltext finalized on: 30 Oct 2001. This page was last modified: 9 Nov 2001.
© 2001 Heldermann Verlag
