Geodesic
Finsler $N$-spinors with real components
Teoretičeskaâ i matematičeskaâ fizika, Tome 183 (2015) no. 3, pp. 359-371

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We study the mathematical objects called Finsler $N$-spinors over the field $\mathbb{R}$ and construct the general algebraic theory of these objects. We show that the Finsler $N$-spinors over the field $\mathbb{R}$ generate two families of $N(N{+}1)/2$- and $N(N{-}1)/2$-dimensional flat pseudo-Finsler spaces. We generalize the epimorphism $SL(2,\mathbb{R})\to O^\uparrow_+(1,2)$ to the case of the group $SL(N,\mathbb{R})$. We consider the examples of Finsler $N$-spinors over the field $\mathbb{R}$ for $N=2,3$ in detail.
Keywords: hyperspinor, Finsler $N$-spinor, group $SL(N,\mathbb R)$.
Mots-clés : pseudo-Finsler space 
@article{TMF_2015_183_3_a1,
     author = {A. V. Solov'ev},
     title = {Finsler $N$-spinors with real components},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {359--371},
     publisher = {mathdoc},
     volume = {183},
     number = {3},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2015_183_3_a1/}
}
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A. V. Solov'ev. Finsler $N$-spinors with real components. Teoretičeskaâ i matematičeskaâ fizika, Tome 183 (2015) no. 3, pp. 359-371. http://geodesic.mathdoc.fr/item/TMF_2015_183_3_a1/