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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 Weyl's theorem on complete reducibility ： ウィキペディア英語版 Weyl's theorem on complete reducibility In algebra, Weyl's theorem on complete reducibility is a fundamental result in the theory of Lie algebra representations. Let $\backslash mathfrak$ be a semisimple Lie algebra over a field of characteristic zero. The theorem states that every finite-dimensional module over $\backslash mathfrak$ is semisimple as a module (i.e., a direct sum of simple modules.) The theorem is a consequence of Whitehead's lemma (see Weibel's homological algebra book). Weyl's original proof was analytic in nature: it famously used the unitarian trick. A Lie algebra is called reductive if its adjoint representation is semisimple. Thus, the theorem says that a semisimple Lie algebra is reductive. (But this can be seen more directly.) == References == * Jacobson, Nathan, ''Lie algebras'', Republication of the 1962 original. Dover Publications, Inc., New York, 1979. ISBN 0-486-63832-4 * 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「Weyl's theorem on complete reducibility」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.