 Solution

In $D$ dimensions the antisymmetric angular momentum tensor has componentsThere are $D(D-1)/2$ independent rotation generators. Together with $D$ translation generators and one time-translation generator, the standard Noether charge enumeration is thereforeThe word independent here counts symmetry generators and tensor components; it needs qualification if it is meant as functional independence of all charges for only two particles in arbitrarily high dimension. In centre-of-mass coordinates, $L=R\wedge P+r\wedge p$. Consequently $P\wedge L\wedge L=0$, a nontrivial identity from dimension five onwards, since $(r\wedge p)\wedge (r\wedge p)=0$. Thus the displayed number is the symmetry-charge count; it is not an assertion that these functions have unrestricted values for a two-particle realization in every $D$.