Scalar products on clifford modules and pseudo-H-type lie algebras
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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.
KeywordsScalar Product Quaternionic Structure Clifford Algebra Real Vector Space Irreducible Module
- [BTV]Berndt J.—Tricerri F.—Vanhecke L.,Geometry of Generalized heisenberg Groups and their Damek-Ricci Harmonic Extensions (to appear).Google Scholar
- [BT]Budinich P.—Trautman A. The Spinorial Chessboard, Springer-Verlag, New York (1988).Google Scholar
- [CDKR2]Cowling M.—Dooley A.—Korányi A.—Ricci F.,An approach to symmetric spaces of rank one via groups of Heisenberg type (to appear).Google Scholar
- [Hu]Husemoller D. Fibre Bundles, Springer-Verlag, New York-Heidelberg-Berlin (1974).Google Scholar