Geodesic
Irreducible carpets of additive subgroups of type $G_2$ over a field of characteristic~$0$
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 15 (2022) no. 5, pp. 610-614

Voir la notice de l'article provenant de la source Math-Net.Ru

It is proved that any irreducible carpet of type $G_2$ over a field $F$ of characteristic $0$, at least one additive subgroup of which is an $R$-module, where $F$ is an algebraic extension of the field $R$, up to conjugation by a diagonal element defines a Chevalley group of type $G_2$ over an intermediate subfield between $R$ and $F$.
Keywords: Chevalley group, carpet of additive subgroups, carpet subgroup. 
@article{JSFU_2022_15_5_a6,
     author = {Yakov N. Nuzhin and Elizaveta N. Troyanskaya},
     title = {Irreducible carpets of additive subgroups of type $G_2$ over a field of characteristic~$0$},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {610--614},
     publisher = {mathdoc},
     volume = {15},
     number = {5},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2022_15_5_a6/}
}
TY  - JOUR
AU  - Yakov N. Nuzhin
AU  - Elizaveta N. Troyanskaya
TI  - Irreducible carpets of additive subgroups of type $G_2$ over a field of characteristic~$0$
JO  - Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
PY  - 2022
SP  - 610
EP  - 614
VL  - 15
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JSFU_2022_15_5_a6/
LA  - en
ID  - JSFU_2022_15_5_a6
ER  - 
%0 Journal Article
%A Yakov N. Nuzhin
%A Elizaveta N. Troyanskaya
%T Irreducible carpets of additive subgroups of type $G_2$ over a field of characteristic~$0$
%J Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
%D 2022
%P 610-614
%V 15
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JSFU_2022_15_5_a6/
%G en
%F JSFU_2022_15_5_a6
Yakov N. Nuzhin; Elizaveta N. Troyanskaya. Irreducible carpets of additive subgroups of type $G_2$ over a field of characteristic~$0$. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 15 (2022) no. 5, pp. 610-614. http://geodesic.mathdoc.fr/item/JSFU_2022_15_5_a6/