Scalar products on Clifford modules and pseudo-H-type Lie algebras

In 1980 A. Kaplan introduced the so called generalised Heisenberg algebras, which are two step nilpotent algebras endowed with an inner product satisfying a compatibility condition with the Lie algebra structure. In this paper we generalize the definition of tk Ka- plan to the case of a nonpositive definite scalar product. In the non-positive definite case the proof of the existence and the classification raise entirely new problems. The natural setting to solve them is that of the theory of Clifford modules.