Existence of the lattice on general H-type groups

الأصل · EN

Let N be a two step nilpotent Lie algebra endowed with non-degenerate scalar product ·,· and let N=V⊕⊥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,·,·ᵥ) is the Clifford module for the Clifford algebra (Z,·,·) such that the homomorphism J (Z,·,·)→(V) is skew symmetric with respect to the scalar product ·,·ᵥ, or in other words the Lie algebra N satisfies conditions of general H-type Lie algebras Ciatti, GKM, then there is a basis with respect to which the structural constants of the Lie algebra N are all ± 1 or 0.