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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 Symmetric Lie group ： ウィキペディア英語版 Orthogonal symmetric Lie algebra In mathematics, an orthogonal symmetric Lie algebra is a pair $(\backslash mathfrak,\; s)$ consisting of a real Lie algebra $\backslash mathfrak$ and an automorphism $s$ of $\backslash mathfrak$ of order $2$ such that the eigenspace $\backslash mathfrak$ of ''s'' corrsponding to 1 (i.e., the set $\backslash mathfrak$ of fixed points) is a compact subalgebra. If "compactness" is omitted, it is called a symmetric Lie algebra. An orthogonal symmetric Lie algebra is said to be ''effective'' if $\backslash mathfrak$ intersects the center of $\backslash mathfrak$ trivially. In practice, effectiveness is often assumed; we do this in this article as well. The canonical example is the Lie algebra of a symmetric space, $s$ being the differential of a symmetry. Every orthogonal symmetric Lie algebra decomposes into a direct sum of ideals "of compact type", "of noncompact type" and "of Euclidean type". == References == * S. Helgason, ''Differential geometry, Lie groups, and symmetric spaces'' 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「Orthogonal symmetric 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.