Geodesic
The existence of root subgroup translated by a given element into its opposite. II
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 40, Tome 531 (2024), pp. 147-151 
I. M. Pevzner. The existence of root subgroup translated by a given element into its opposite. II. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 40, Tome 531 (2024), pp. 147-151. http://geodesic.mathdoc.fr/item/ZNSL_2024_531_a8/
@article{ZNSL_2024_531_a8,
     author = {I. M. Pevzner},
     title = {The existence of root subgroup translated by a given element into its opposite. {II}},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {147--151},
     year = {2024},
     volume = {531},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2024_531_a8/}
}
TY  - JOUR
AU  - I. M. Pevzner
TI  - The existence of root subgroup translated by a given element into its opposite. II
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2024
SP  - 147
EP  - 151
VL  - 531
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2024_531_a8/
LA  - ru
ID  - ZNSL_2024_531_a8
ER  - 
%0 Journal Article
%A I. M. Pevzner
%T The existence of root subgroup translated by a given element into its opposite. II
%J Zapiski Nauchnykh Seminarov POMI
%D 2024
%P 147-151
%V 531
%U http://geodesic.mathdoc.fr/item/ZNSL_2024_531_a8/
%G ru
%F ZNSL_2024_531_a8

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

Let $\Phi$ be a simply-laced root system, $|K|>5$, $G = G_{ad}(\Phi,K)$ the adjoint group of type $\Phi$ over $K$. Then for every non-trivial element $g\in G$ there exists a root element $x$ of the Lie algebra of $G$ such that $x$ and $gx$ are opposite.

[1] A. Borel, “Svoistva i lineinye predstavleniya grupp Shevalle”, Seminar po algebraicheskim gruppam, Mir, M., 1973, 9–59

[2] N. Burbaki, Gruppy i algebry Li. Glavy IV–VI, Mir, M., 1972 | MR

[3] N. Burbaki, Gruppy i algebry Li. Glavy VII–VIII, Mir, M., 1978 | MR

[4] I. M. Pevzner, “Geometriya kornevykh elementov v gruppakh tipa $\mathrm{E}_6$”, Algebra i analiz, 23:3 (2011), 261–309

[5] I. M. Pevzner, “Shirina grupp tipa ${\mathrm{E}}_{6}$ otnositelno mnozhestva kornevykh elementov, I”, Algebra i analiz, 23:5 (2011), 155–198

[6] I. M. Pevzner, “Shirina grupp tipa ${\mathrm{E}}_{6}$ otnositelno mnozhestva kornevykh elementov, II”, Zap. nauchn. semin. POMI, 386, 2011, 242–264

[7] I. M. Pevzner, “Suschestvovanie kornevoi podgruppy, kotoruyu dannyi element perevodit v protivopolozhnuyu”, Zap. nauchn. semin. POMI, 460, 2017, 190–202

[8] T. A. Springer, “Lineinye algebraicheskie gruppy”, Algebraicheskaya geometriya – 4, Itogi nauki i tekhn. Ser. Sovrem. problemy mat. Fundam. napravleniya, 55, VINITI, M., 1989, 5–136

[9] R. Steinberg, Lektsii o gruppakh Shevalle, Mir, M., 1975

[10] Dzh. Khamfri, Lineinye algebraicheskie gruppy, Nauka, M., 1980

[11] Dzh. Khamfri, Vvedenie v teoriyu algebr Li i ikh predstavlenii, MTsNMO, M., 2003

[12] T. A. Springer, Linear algebraic groups, Progress in Mathematics, 9, Birkhäuser Boston Inc., Boston, 1998 | MR

[13] N. A. Vavilov, E. B. Plotkin, “Chevalley groups over commutative rings. I. Elementary calculations”, Acta Applicandae Math., 45 (1996), 73–115 | DOI | MR