Geodesic
Irreducible carpets of Lie type $B_l$, $C_l$ and $F_4$ over fields
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 20 (2023) no. 1, pp. 124-131

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V.M. Levchuk described irreducible carpets of Lie type of rank greater than $1$ over the field $F$, at least one additive subgroup of which is an $R$-module, where $F$ is an algebraic extension of the field $R$, in assumption that the characteristic of the field $F$ is different from $0$ and $2$ for the types $B_l$, $C_l$, $F_4$, and for the type $G_2$ it is different from $0, 2$ and $3$ (Algebra i Logika, 1983, 22, no. 5). It turned out that, up to conjugation by a diagonal element, all additive subgroups of such carpets coincide with one intermediate subfield between $R$ and $F$. We solve a similar problem for carpets of types $B_l$, $C_l$, $F_4$ over a field of characteristic $0$ and $2$. It turned out that carpets appear in characteristic $2$, which are parameterized by a pair of additive subgroups, and for types $B_l$ and $C_l$ one of these two additive subgroups may not be a field.
Keywords: Chevalley group, carpet of additive subgroups, carpet subgroup. 
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     title = {Irreducible carpets of {Lie} type $B_l$, $C_l$ and $F_4$ over fields},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
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A. O. Likhacheva; Ya. N. Nuzhin. Irreducible carpets of Lie type $B_l$, $C_l$ and $F_4$ over fields. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 20 (2023) no. 1, pp. 124-131. http://geodesic.mathdoc.fr/item/SEMR_2023_20_1_a3/