Finslerian \(N\)-spinors: algebra. (Q5947388)

In this paper authors develop a theory of objects that they call Finslerian \(N\)-spinors. These are elements of a \(N\)-dimensional space, denoted \(\mathbf{FS}^{N}\) (over the complex field \(\mathbb{C}\)0, where it is defined a antisymmetric \(N\)-functional, which takes values on \(\mathbb{C}\). In the case \(N=2\), it is shown that that definition agrees with Weyl spinors. The authors, quote that these objects appeared within the so called relational theory of spacetime developed by them in 1996. Unfortunately the references were not printed in the paper under review. The authors notice that these objects have also been studied by D. R. Finkelstein [Phys. Rev. Lett. 56, No. 15, 1532--1533 (1986; Zbl 1106.82310)] under the name hyperspinors. It should be added that they also appeared in the work of M. Barnabei, A. Brini and G.-C. Rota [J. Algebra 96, No. 1, 120--160 (1985; Zbl 0585.15005)], who gave a very complete study of this structure under the name of Peano space.