Classification of real trivectors in dimension nine

0556583 - MÚ 2023 RIV US eng J - Článek v odborném periodiku
Borovoi, M. - de Graaf, W. A. - Le, Hong-Van
Classification of real trivectors in dimension nine.
Journal of Algebra. Roč. 603, August 1 (2022), s. 118-163. ISSN 0021-8693. E-ISSN 1090-266X
Grant CEP: GA ČR(CZ) GC18-01953J
Institucionální podpora: RVO:67985840
Klíčová slova: trivector * graded Lie algebra * real Galois cohomology
Obor OECD: Pure mathematics
Impakt faktor: 0.9, rok: 2022
Způsob publikování: Omezený přístup
https://doi.org/10.1016/j.jalgebra.2022.04.003

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 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.
Trvalý link: http://hdl.handle.net/11104/0330753