Annali di Matematica Pura ed Applicata

, Volume 178, Issue 1, pp 1–31 | Cite as

Scalar products on clifford modules and pseudo-H-type lie algebras

  • Paolo Ciatti


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 A. Kaplan 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.


Scalar Product Quaternionic Structure Clifford Algebra Real Vector Space Irreducible Module 
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© Fondazione Annali di Matematica Pure ed Applicata 2000

Authors and Affiliations

  • Paolo Ciatti
    • 1
  1. 1.Dipartimento di MatematicaPolitecnico di TorinoTorino

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