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TMF, 2015, Volume 183, Number 3, Pages 359–371 (Mi tmf8812)  

Finsler $N$-spinors with real components

A. V. Solov'ev

Lomonosov Moscow State University, Moscow, Russia, Faculty of Physics

Abstract: 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, pseudo-Finsler space, group $SL(N,\mathbb R)$

DOI: https://doi.org/10.4213/tmf8812

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English version:
Theoretical and Mathematical Physics, 2015, 183:3, 756–767

Bibliographic databases:

Received: 29.10.2014
Revised: 05.02.2015

Citation: A. V. Solov'ev, “Finsler $N$-spinors with real components”, TMF, 183:3 (2015), 359–371; Theoret. and Math. Phys., 183:3 (2015), 756–767

Citation in format AMSBIB
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  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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