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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 Whitehead's lemma (Lie algebras) ： ウィキペディア英語版 Whitehead's lemma (Lie algebras) In algebra, Whitehead's lemma on a Lie algebra representation is an important step toward the proof of Weyl's theorem on complete reducibility. Let $\backslash mathfrak$ be a semisimple Lie algebra over a field of characteristic zero, ''V'' a finite-dimensional module over it and $f:\; \backslash mathfrak\; \backslash to\; V$ a linear map such that $f((y))\; =\; xf(y)\; -\; yf(x)$. The lemma states that there exists a vector ''v'' in ''V'' such that $f(x)\; =\; xv$ for all ''x''. The lemma may be interpreted in terms of Lie algebra cohomology. The proof of the lemma uses a Casimir element. == 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「Whitehead's lemma (Lie algebras)」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.