The abstract quantal algebra developed in Part I of the present work describes the common structure of the two known mechanics, classical and quantum. By itself, however, it is not physics. It is a mathematical object, or, as some might say, it is only mathematics, a valid objection if quantal algebra were meant to be an end in itself, for physics is not in abstract theories, but in their concrete realizations. Hence, the immediate question is whether at least one new concrete realization of the quantal algebra exists, for it is among these that a physically valid generalization of quantum mechanics might be found. The search for all realizations of an abstract theory is known in mathematics as structure theory, or the classification problem. Usually difficult, it is relatively easy in our case because the foundations have already been laid in Cartan\u27s classification of the semi-simple Lie algebras. Since the quantal algebra contains a Lie algebra, we only need to adapt the standard work to our case by imposing some additional conditions. The result is that the semi-simple quantal algebra has exactly two realizations. Expressed in terms of groups, one is the infinite family of unitary groups, SU( n) , (i.e., standard quantum mechanics), the other is an exceptional solution, the group SO( 2,4). Classical mechanics does not appear as a solution because the requirement of semi-simplicity eliminates the canonical group. Thus, if quantum mechanics can be generalized, the generalization is somehow related to the group SO( 2,4) , and as this group contains the relativistic space-time structure, it appears that an inherently covariant generalization might be possible.Apstraktna kvantalna algebra razvijena u Dijelu I ovog rada opisuje zajedničku strukturu dviju poznatih mehanika, klasične i kvantne. Sama ta algebra nije fizika. Ona je matematički sustav, ili, kako bi neki mogli reći samo matematika, točan prigovor ako bi kvantalna algebra bila sama sebi ciljem, jer fizika nije u apstraktnim teorijama već u njihovim stvarnim realizacijama. Stoga se pitamo, postoji li bar jedna stvarna realizacija kvantalne algebre, jer medu tima mogle bi se naći generalizacije kvantne mehanike koje vrijede u fizici. Potraga za realizacijama apstraktne teorije je poznata pod nazivom strukturna teorija ili klasifikacijski problem. To je obično vrlo težak zadatak, no u ovom je slučaju relativno lagan jer su osnove već postavljene Cartanovom klasifikacijom polujednostavnih Lievih algebri. Budući da kvantalna algebra sadrži jednu Lievu algebru, trebamo samo primijeniti standardne rezultate postavljanjem dodatnih uvjeta. Ishod je toga da polujednostavna kvantalna algebra ima točno dvije realizacije. Izraženo preko teorije grupa, jedna je beskonačna familija unitarnih grupa, SO (n), (tj., standardna kvantna mehanika), a druga je posebno rješenje, SO (2, 4). Klasična mehanika nije rješenje jer zahtjev polujednostavnosti uklanja kanonsku grupu. Stoga, ako se kvantna mehanika može generalizirati. ta je generalizacija na neki način u svezi s grupom SO (2, 4). Ta grupa sadrži relativističku strukturu prostora–vremena, pa se čini da je moguća suštinski kovarijantna generalizacija
