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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Nilpotent orbit ： ウィキペディア英語版 Nilpotent orbit In mathematics, nilpotent orbits are generalizations of nilpotent matrices that play an important role in representation theory of real and complex semisimple Lie groups and semisimple Lie algebras. == Definition == An element ''X'' of a semisimple Lie algebra ''g'' is called nilpotent if its adjoint endomorphism : ''ad X'': ''g'' → ''g'',   ''ad X''(''Y'') = () is nilpotent, that is, (''ad X'')''n'' = 0 for large enough ''n''. Equivalently, ''X'' is nilpotent if its characteristic polynomial ''p''''ad X''(''t'') is equal to ''t''dim ''g''. A semisimple Lie group or algebraic group ''G'' acts on its Lie algebra via the adjoint representation, and the property of being nilpotent is invariant under this action. A nilpotent orbit is an orbit of the adjoint action such that any (equivalently, all) of its elements is (are) nilpotent. 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「Nilpotent orbit」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.