Тип публикации: статья из журнала
Год издания: 2023
Идентификатор DOI: 10.1134/s0037446623060198
Ключевые слова: Chevalley group, carpet of additive subgroups, carpet subgroup, root system, 512.54, mathematics, general
Аннотация: We consider the irreducible carpets $ \mathfrak{A}=\{\mathfrak{A}_{r}:\ r\in\Phi\} $ of type $ F_{4} $ over an algebraical extension $ K $ of a field $ R $ such that all additive subgroups $ \mathfrak{A}_{r} $ are $ R $ -modules. The carpets, parametrized by a pair of additive subgroups, appear only in characteristic 2. This pair oПоказать полностьюf additive subgroups presents (possibly different) fields up to conjugation by a diagonal element in the corresponding Chevalley group. Moreover, we establish that such carpets $ \mathfrak{A} $ are closed. Using Levchuk’s description of the irreducible carpets of Lie type of rank greater than 1 over $ K $ , we show that all additive subgroups of the carpets coincide with an intermediate subfield between $ R $ and $ K $ of the carpets of types $ B_{l} $ , $ C_{l} $ , and $ F_{4} $ in case of the characteristic of $ K $ is not 0 and 2 whereas it is neither 0, 2, nor 3 for type $ G_{2} $ up to conjugation by a diagonal element.
Журнал: Siberian Mathematical Journal
Выпуск журнала: Т.64, №6
Номера страниц: 1472-1476
ISSN журнала: 00374466
Место издания: Новосибирск
Издатель: Pleiades Publishing, Ltd. (Плеадес Паблишинг, Лтд)