Existence of Lattices on General H-Type Groups

Let N be a two step nilpotent Lie algebra endowed with non-degenerate scalar product [center dot,center dot] and let N = V circle plus(perpendicular to) Z, where Z is the center of the Lie algebra and V its orthogonal complement with respect to the scalar product. We prove that if (V, [center dot,center dot]v) is the Clifford module for the Clifford algebra Cl(Z, [center dot,center dot]z) such that the homomorphism J: Cl(Z, (center dot,center dot)z) --> End(V) is skew symmetric with respect to the scalar product [center dot,center dot]v, or in other words the Lie algebra N satisfies conditions of general H-type Lie algebras [6, 13], then there is a basis with respect to which the structural constants of the Lie algebra N are all +/- 1 or 0.