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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 Reductive Lie algebra ： ウィキペディア英語版 Reductive Lie algebra In mathematics, a Lie algebra is reductive if its adjoint representation is completely reducible, whence the name. More concretely, a Lie algebra is reductive if it is a direct sum of a semisimple Lie algebra and an abelian Lie algebra: $\backslash mathfrak\; =\; \backslash mathfrak\; \backslash oplus\; \backslash mathfrak;$ there are alternative characterizations, given below. == Examples == The most basic example is the Lie algebra $\backslash mathfrak\_n$ of $n\; \backslash times\; n$ matrices with the commutator as Lie bracket, or more abstractly as the endomorphism algebra of an ''n''-dimensional vector space, $\backslash mathfrak(V).$ This is the Lie algebra of the general linear group GL(''n''), and is reductive as it decomposes as $\backslash mathfrak\_n\; =\; \backslash mathfrak\_n\; \backslash oplus\; \backslash mathfrak,$ corresponding to traceless matrices and scalar matrices. Any semisimple Lie algebra or abelian Lie algebra is ''a fortiori'' reductive. Over the real numbers, compact Lie algebras are reductive. 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「Reductive 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.