Classification of pseudo $H$-type algebras

TL;DR

This paper provides a partial classification of pseudo $H$-type algebras with minimal admissible Clifford modules and characterizes when certain subspaces are strongly bracket generating.

Contribution

It offers new classification results for pseudo $H$-type algebras and analyzes the conditions for strong bracket generation related to Clifford modules.

Findings

Subspace $rak{v}_{r,s}$ is strongly bracket generating iff $r=0$ or $s=0$

Partial classification of pseudo $H$-type algebras with minimal modules

Discussion on classification related to non-equivalent irreducible Clifford modules

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.