With the Poincar\'e group $\mathbf{ R}^{ 3,\,1}\rtimes O(3,\,1)$ as the model of departure, we focus, for $n=p+q$, $p+q\ge 4$, on the affine indefinite orthogonal group $\mathbf{ R}^{ p,q}\rtimes SO(p,\,q)$. Denote by $\mathfrak{ h}_{ p,\,q}$ the Lie algebra of the affine indefinite orthogonal group. We compute the Leibniz cohomology of $\mathfrak{ h}_{ p,\,q}$ with adjoint coefficients, written $HL^*(\mathfrak{ h}_{ p,\,q};\,\mathfrak{ h}_{ p,\,q})$. We calculate several indefinite orthogonal invariants, and $\mathfrak{ h}_{ p,\,q} $-invariants and provide the Leibniz cohomology in terms of these invariants.
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