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Corpus ID: 235265879

Real graded Lie algebras, Galois cohomology, and classification of trivectors in R^9

@inproceedings{Borovoi2021RealGL,
title={Real graded Lie algebras, Galois cohomology, and classification of trivectors in R^9},
author={Mikhail Borovoi and Willem A. de Graaf and H{\^o}ng V{\^a}n L{\^e}},
year={2021}
}

In this paper we classify real trivectors in dimension 9. The corresponding classification over the field C of complex numbers was done by Vinberg and Elashvili in 1978. One of the main tools used for their classification was the construction of the representation of SL(9,C) on the space of complex trivectors of C^9 as a theta-representation corresponding to a Z/3Z-grading of the simple complex Lie algebra of type E8. This divides the trivectors into three groups: nilpotent, semisimple, and… Expand

We classify states of four rebits, that is, we classify the orbits of the group Ĝ(R) = SL(2,R) in the space (R). is is the real analogon of the well-known SLOCC operations in quantum information… Expand

Let G be a linear algebraic group over the field of real numbers R, and let Y be a right homogeneous space of G. We wish to find a real point of Y or to prove that Y has no real points. We describe a… Expand