Тип публикации: статья из журнала
Год издания: 2023
Идентификатор DOI: 10.33048/semi.2023.20.011
Ключевые слова: Chevalley group, carpet of additive subgroups, carpet subgroup
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 Показать полностьюdifferent 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.
Журнал: Сибирские электронные математические известия
Выпуск журнала: Т. 20, № 1
Номера страниц: 124-131
ISSN журнала: 18133304
Место издания: Новосибирск
Издатель: Институт математики им. С.Л. Соболева СО РАН