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Classification of real trivectors in dimension nine

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arxiv 2108.00790 v1 pith:OUWAXFMP submitted 2021-08-02 math.RT math.DGmath.GRmath.RA

Classification of real trivectors in dimension nine

classification math.RT math.DGmath.GRmath.RA
keywords classificationtrivectorscomplexcorrespondingdimensionrealalgebraclassify
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We classify real trivectors in dimension 9. The corresponding classification over the field C of complex numbers was obtained 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 E_8. This divides the trivectors into three groups: nilpotent, semisimple, and mixed trivectors. Our classification follows the same pattern. We use Galois cohomology, first and second, to obtain the classification over R.

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