On linear resolvability of universal quantum dimensions

In the study of finite (Vassiliev’s) knot invariants, Vogel introduced so-called universal parameters, belonging to projective plane, in particular parametrizing simple Lie algebras by Vogel’s table. Subsequently, a number quantities, such as some invariants and (quantum) dimensions algebras, have been represented terms these i.e., form. We prove that at points from table all known quantum dimension formulae are linearly resolvable, yield answers even if singular, provided one restricts them appropriate lines. show same phenomenon takes place for another three distinguished plane — [Formula: see text] text]. also examine on linear resolvability remaining 48 which correspond text]-objects. Among them, were found be regular formulae. Two happen sharing remarkable similarity with namely, integer-valued outputs (dimensions) indicated classical limit.