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Quasi-split group : ウィキペディア英語版 | Quasi-split group In mathematics, a quasi-split group over a field is a reductive group with a Borel subgroup defined over the field. Simply connected quasi-split groups over a field correspond to actions of the absolute Galois group on a Dynkin diagram. ==Examples== All split groups (those with a split maximal torus) are quasi-split. These correspond to quasi-split groups where the action of the Galois group on the Dynkin diagram is trivial. showed that all simple algebraic groups over finite fields are quasi-split. Over the real numbers, the quasi-split groups include the split groups and the complex groups, together with the orthogonal groups ''O''''n'',''n''+2, the unitary groups ''SU''''n'',''n'' and ''SU''''n'',''n''+1, and the form of ''E''6 with signature 2.
抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)』 ■ウィキペディアで「Quasi-split group」の詳細全文を読む
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