Classification of real trivectors in dimension nine

Mikhail Borovoi, Willem A. de Graaf*, Hông Vân Lê

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


In this paper 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 C9 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 mixed trivectors. Our classification follows the same pattern. We use Galois cohomology, first and second, to obtain the classification over R.

Original languageEnglish
Pages (from-to)118-163
Number of pages46
JournalJournal of Algebra
StatePublished - 1 Aug 2022


FundersFunder number
Australian Research Council18-01953J, DP190100317, 67985840
Grantová Agentura České Republiky
Israel Science Foundation870/16


    • Graded Lie algebra
    • Real Galois cohomology
    • Trivector


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