1Dept. of Mathematics, LaGuardia Community College, City University of New York, 31-10 Thomson Avenue, Long Island City, NY 11101, U.S.A. 2Graduate Center, City University, 365 Fifth Avenue, New York, NY 10016, U.S.A. 3We prove that every 4-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 5-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 6-type groups. 7[
Journal of Lie Theory, Tome 12 (2002) no. 1, pp. 69-79
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Gordon Crandall; Józef 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/JOLT_2002_12_1_a4/
@article{JOLT_2002_12_1_a4,
author = {Gordon Crandall and J\'ozef 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/JOLT_2002_12_1_a4/}
}
TY - JOUR
AU - Gordon Crandall
AU - Józef Dodziuk
TI - Integral Structures on H-type Lie Algebras
JO - Journal of Lie Theory
PY - 2002
SP - 69
EP - 79
VL - 12
IS - 1
UR - http://geodesic.mathdoc.fr/item/JOLT_2002_12_1_a4/
ID - JOLT_2002_12_1_a4
ER -
%0 Journal Article
%A Gordon Crandall
%A Józef Dodziuk
%T Integral Structures on H-type Lie Algebras
%J Journal of Lie Theory
%D 2002
%P 69-79
%V 12
%N 1
%U http://geodesic.mathdoc.fr/item/JOLT_2002_12_1_a4/
%F JOLT_2002_12_1_a4
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.
