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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 Radical of a Lie algebra ： ウィキペディア英語版 Radical of a Lie algebra In the mathematical field of Lie theory, the radical of a Lie algebra $\backslash mathfrak$ is the largest solvable ideal of $\backslash mathfrak.$〔.〕 == Definition == Let $k$ be a field and let $\backslash mathfrak$ be a finite-dimensional Lie algebra over $k$. There exists a unique maximal solvable ideal, called the ''radical,'' for the following reason. Firstly let $\backslash mathfrak$ and $\backslash mathfrak$ be two solvable ideals of $\backslash mathfrak$. Then $\backslash mathfrak+\backslash mathfrak$ is again an ideal of $\backslash mathfrak$, and it is solvable because it is an extension of $(\backslash mathfrak+\backslash mathfrak)/\backslash mathfrak\backslash simeq\backslash mathfrak/(\backslash mathfrak\backslash cap\backslash mathfrak)$ by $\backslash mathfrak$. Now consider the sum of all the solvable ideals of $\backslash mathfrak$. It is nonempty since $\backslash$ is a solvable ideal, and it is a solvable ideal by the sum property just derived. Clearly it is the unique maximal solvable ideal. 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「Radical of a 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.