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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 E11 (mathematics) ： ウィキペディア英語版 En (Lie algebra) In mathematics, especially in Lie theory, E''n'' is the Kac–Moody algebra whose Dynkin diagram is a bifurcating graph with three branches of length 1,2, and ''k'', with ''k''=''n-4''. In some older books and papers, ''E''2 and ''E''4 are used as names for ''G''2 and ''F''4. ==Finite-dimensional Lie algebras== The En group is similar to the An group, except the nth node is connected to the 3rd node. So the Cartan matrix appears similar, -1 above and below the diagonal, except for the last row and column, have -1 in the third row and column. The determinant of the Cartan matrix for En is 9-''n''. *E3 is another name for the Lie algebra ''A''1''A''2 of dimension 11, with Cartan determinant 6. *: -1 & 2 & 0 \\ 0 & 0 & 2 \end\right ) *E4 is another name for the Lie algebra ''A''4 of dimension 24, with Cartan determinant 5. *: -1 & 2 & -1& 0 \\ 0 & -1 & 2 & -1 \\ 0 & 0 & -1 & 2 \end\right ) *E5 is another name for the Lie algebra ''D''5 of dimension 45, with Cartan determinant 4. *: -1 & 2 & -1& 0 & 0 \\ 0 & -1 & 2 & -1 & -1 \\ 0 & 0 & -1 & 2 & 0 \\ 0 & 0 & -1 & 0 & 2 \end\right ) *E6 is the exceptional Lie algebra of dimension 78, with Cartan determinant 3. *: -1 & 2 & -1& 0 & 0 & 0 \\ 0 & -1 & 2 & -1 & 0 & -1 \\ 0 & 0 & -1 & 2 & -1 & 0 \\ 0 & 0 & 0 & -1 & 2 & 0 \\ 0 & 0 & -1 & 0 & 0 & 2 \end\right ) *E7 is the exceptional Lie algebra of dimension 133, with Cartan determinant 2. *: -1 & 2 & -1& 0 & 0 & 0 & 0 \\ 0 & -1 & 2 & -1 & 0 & 0 & -1 \\ 0 & 0 & -1 & 2 & -1 & 0 & 0 \\ 0 & 0 & 0 & -1 & 2 & -1 & 0 \\ 0 & 0 & 0 & 0 & -1 & 2 & 0 \\ 0 & 0 & -1 & 0 & 0 & 0 & 2 \end\right ) *E8 is the exceptional Lie algebra of dimension 248, with Cartan determinant 1. *: -1 & 2 & -1& 0 & 0 & 0 & 0 & 0 \\ 0 & -1 & 2 & -1 & 0 & 0 & 0 & -1 \\ 0 & 0 & -1 & 2 & -1 & 0 & 0 & 0 \\ 0 & 0 & 0 & -1 & 2 & -1 & 0 & 0 \\ 0 & 0 & 0 & 0 & -1 & 2 & -1 & 0 \\ 0 & 0 & 0 & 0 & 0 & -1 & 2 & 0 \\ 0 & 0 & -1 & 0 & 0 & 0 & 0 & 2 \end\right ) 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「En (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.