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Изв. АН СССР. Сер. матем., 1975, том 39, выпуск 2, страницы 315–362
(Mi izv1833)
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Эта публикация цитируется в 78 научных статьях (всего в 78 статьях)
Классификация кватернионных пространств с транзитивной разрешимой группой движений
Д. В. Алексеевский
Аннотация:
В работе получена полная классификация кватернионных римановых пространств
(т.е. римановых пространств $\mathscr V^n$ с группой голономии $\Gamma\subset Sp(1)\cdot Sp(m)$, $n=4m$), допускающих транзитивную разрешимую группу движений. Оказывается, что ранг таких пространств не превосходит четырех и пространства $\mathscr V^n$ ранга меньше четырех симметричны. Пространства $\mathscr V^n$ ранга четыре находятся в естественном взаимно однозначном соответствии с клиффордовыми модулями в смысле Атьи–Ботта–Шапиро. При этом простейшим клиффордовым модулям, которые соответствуют алгебрам с делением, отвечают симметрические пространства особых групп Ли. Остальным клиффордовым модулям, которые получаются из простейших с помощью операций тензорного произведения, прямой суммы и ограничения, отвечают несимметрические пространства.
Библиография: 17 названий.
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Англоязычная версия:
Mathematics of the USSR-Izvestiya, 1975, 9:2, 297–339
Реферативные базы данных:
 
УДК:
513.6
MSC: Primary 53C15, 53C20, 53C25, 53C30; Secondary 53C35, 53C55
Поступило в редакцию: 12.05.1974
Образец цитирования:
Д. В. Алексеевский, “Классификация кватернионных пространств с транзитивной разрешимой группой движений”, Изв. АН СССР. Сер. матем., 39:2 (1975), 315–362; Math. USSR-Izv., 9:2 (1975), 297–339
Цитирование в формате AMSBIB
\RBibitem{Ale75}
\by Д.~В.~Алексеевский
\paper Классификация кватернионных пространств с~транзитивной разрешимой группой движений
\jour Изв. АН СССР. Сер. матем.
\yr 1975
\vol 39
\issue 2
\pages 315--362
\mathnet{http://mi.mathnet.ru/izv1833}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=402649}
\zmath{https://zbmath.org/?q=an:0309.53045}
\transl
\jour Math. USSR-Izv.
\yr 1975
\vol 9
\issue 2
\pages 297--339
\crossref{https://doi.org/10.1070/IM1975v009n02ABEH001479}
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