Библиографическое описание:НЕПРИВОДИМЫЕ КОВРЫ ЛИЕВА ТИПА Bl, Cl И F4 НАД ПОЛЯМИ : научное издание / А. О. ЛИХАЧЕВА, Я. Н. НУЖИН. - Текст : непосредственный // Сибирские электронные математические известия. - 2023. - Т. 20, № 1. - С. 124-131. - Работа поддержана РНФ (грант 22-21-00733). - ISSN 1813-3304, DOI 10.33048/semi.2023.20.011.
Аннотация: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-modnle. 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 Bl, Cl, F4, and for the type G2 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 Bl, Cl, F4 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 Bl and Cl one of these two additive subgroups may not be a field.
