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Pseudo $H$-type Lie algebras are a special class of 2-step nilpotent metricLie algebras, intimately related to Clifford algebras $\Cl_{r,s}$. In this workwe propose the classification method for integral orthonormal structures ofpseudo $H$-type Lie algebras. We apply this method for the full classificationof these structures for $r\in\{1,\ldots,16\}$, $s\in \{0,1\}$ and irreducibleClifford modules. The latter cases form the basis for the further extensions bymaking use of the Atiyah-Bott periodicity. The existence of integral structuresgives rise to the integral discrete uniform subgroups of the pseudo $H$-typeLie groups.

Invariant integral structures in pseudo $H$-type Lie algebras: construction and classification