Classification of pseudo $H$-type algebras

Abstract

We present a partial classification of the pseudo $H$-type algebras with minimal admissible Clifford modules. Furthermore, we prove that the subspace ${\mathfrak{v}}_{r,s}$ of ${\mathfrak{n}}_{r,s}$ is strongly bracket generating if and only if $r=0$ or $s=0$. Additionally, we discuss the classification of pseudo $H$-type algebras related to non-equivalent irreducible Clifford modules.

41 pages, 0 figures