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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 Linear Lie algebra ： ウィキペディア英語版 Linear Lie algebra In algebra, a linear Lie algebra is a subalgebra $\backslash mathfrak$ of the Lie algebra $\backslash mathfrak(V)$ consisting of endomorphisms of a vector space ''V''. In other words, a linear Lie algebra is the image of a Lie algebra representation. Any Lie algebra is a linear Lie algebra in the sense that there is always a faithful representation of $\backslash mathfrak$ (in fact, on a finite-dimensional vector space by Ado's theorem if $\backslash mathfrak$ is itself finite-dimensional.) Let ''V'' be a finite-dimensional vector space over a field of characteristic zero and $\backslash mathfrak$ a subalgebra of $\backslash mathfrak(V)$. Then ''V'' is semisimple as a module over $\backslash mathfrak$ if and only if (i) it is a direct sum of the center and a semisimple ideal and (ii) the elements of the center are diagonalizable (over some extension field). == Notes == 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「Linear Lie algebra」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.