翻訳と辞書 Words near each other ・ Semirostrum ・ Semirâma ・ Semis ・ Semisalsa galilaea ・ Semisalsa stagnorum ・ Semiset ・ Semisi Masirewa ・ Semisi Naevo ・ Semisi Sika ・ Semisi Tapueluelu ・ Semisi Taulava ・ Semisi Telefoni ・ Semisi Tora ・ Semisimple algebra ・ Semisimple algebraic group ・ Semisimple Lie algebra ・ Semisimple module ・ Semisoft sign ・ Semisonic ・ Semisopochnoi Island ・ Semisphaeria ・ Semispherical drum ・ Semispinalis capitis ・ Semispinalis cervicis ・ Semispinalis muscles ・ Semispinalis thoracis ・ Semistable abelian variety ・ Semisulcospira ・ Semisulcospira decipiens ・ Semisulcospira diminuta Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Semisimple Lie algebra ： ウィキペディア英語版 Semisimple Lie algebra In mathematics, a Lie algebra is semisimple if it is a direct sum of simple Lie algebras, i.e., non-abelian Lie algebras $\backslash mathfrak\; g$ whose only ideals are and $\backslash mathfrak\; g$ itself. Throughout the article, unless otherwise stated, $\backslash mathfrak\; g$ is a finite-dimensional Lie algebra over a field of characteristic 0. The following conditions are equivalent: *$\backslash mathfrak\; g$ is semisimple *the Killing form, κ(x,y) = tr(ad(''x'')ad(''y'')), is non-degenerate, *$\backslash mathfrak\; g$ has no non-zero abelian ideals, *$\backslash mathfrak\; g$ has no non-zero solvable ideals, * The radical (maximal solvable ideal) of $\backslash mathfrak\; g$ is zero. == Examples == Examples of semisimple Lie algebras, with notation coming from classification by Dynkin diagrams, are: * $A\_n:$ $\backslash mathfrak\; \_$, the special linear Lie algebra. * $B\_n:$ $\backslash mathfrak\_$, the odd-dimensional special orthogonal Lie algebra. * $C\_n:$ $\backslash mathfrak\; \_$, the symplectic Lie algebra. * $D\_n:$ $\backslash mathfrak\_$, the even-dimensional special orthogonal Lie algebra. These Lie algebras are numbered so that ''n'' is the rank. Except certain exceptions in low dimensions, many of these are simple Lie algebras, which are ''a fortiori'' semisimple. These four families, together with five exceptions (E6, E7, E8, F4, and G2), are in fact the ''only'' simple Lie algebras over the complex numbers. 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「Semisimple 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.