Classification of real trivectors in dimension nine
Representation Theory
2021-08-03 v1 Differential Geometry
Group Theory
Rings and Algebras
Abstract
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.
Cite
@article{arxiv.2108.00790,
title = {Classification of real trivectors in dimension nine},
author = {Mikhail Borovoi and Willem A. de Graaf and Hông Vân Lê},
journal= {arXiv preprint arXiv:2108.00790},
year = {2021}
}
Comments
Shortened version (submitted to a journal) of arXiv:2106.00246 [math.RT]; 38 pages