Leibniz cohomology with adjoint coefficients

Abstract

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