Leibniz cohomology with adjoint coefficients

With the Poincaré group R3, 1⋊O(3,1) as the model of departure, we focus, for n=p+q, p+q≥4, on the affine indefinite orthogonal group Rp,q⋊SO(p,q). Denote by hp, q the Lie algebra of the affine indefinite orthogonal group. We compute the Leibniz cohomology of hp, q with adjoint coefficients, written HL*(hp, q;hp, q). We calculate several indefinite orthogonal invariants, and hp, q-invariants.