We consider a family of nilpotent Lie algebras attached to Clifford algebras and their ``admissible'' modules. These are called pseudo $H$-type algebras. Our purpose is to explain how to classify them and give a complete classification table (mod Bott periodicity). Then we mention an application to the construction of isospectral non-diffeomorphic family of nilmanifolds of arbitrary given number with respect to the both sense of the Laplacian and sub-Laplacian.

This is a joint work with prof. Irina Markina at University of Bergen, Norway.]

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