On the Product Rule for the Hyperbolic Scator Algebra.

Scator set, introduced by Fernandez-Guasti and Zaldivar, is endowed with a very peculiar non-distributive product. In this paper we consider the scator space of dimension1+2and the so called fundamental embedding which maps the subset of scators with non-zero scalar component into 4-dimensional space endowed with a natural distributive product. The original definition of the scator product is induced in a straightforward way. Moreover, we propose an extension of the scator product on the whole scator space, including all scators with vanishing scalar component.