The alternative torus and the structure of elliptic quasi-simple Lie algebras of type $A\sb 2$

We present the complete classification of the tame irreducible elliptic quasi-simple Lie algebras of type ${A_2}$, and in particular, specialize on the case where the coordinates are not associative. Here the coordinates are Cayley-Dickson algebras over Laurent polynomial rings in $\nu \geqslant 3$ variables, which we call alternative tori. In giving our classification we need to present much information on these alternative tori and the Lie algebras coordinatized by them.