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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 Cartan decomposition ： ウィキペディア英語版 Cartan decomposition The Cartan decomposition is a decomposition of a semisimple Lie group or Lie algebra, which plays an important role in their structure theory and representation theory. It generalizes the polar decomposition or singular value decomposition of matrices. Its history can be traced to the 1880s work of Élie Cartan and Wilhelm Killing. () == Cartan involutions on Lie algebras == Let $\backslash mathfrak$ be a real semisimple Lie algebra and let $B(\backslash cdot,\backslash cdot)$ be its Killing form. An involution on $\backslash mathfrak$ is a Lie algebra automorphism $\backslash theta$ of $\backslash mathfrak$ whose square is equal to the identity. Such an involution is called a Cartan involution on $\backslash mathfrak$ if $B\_\backslash theta(X,Y)\; :=\; -B(X,\backslash theta\; Y)$ is a positive definite bilinear form. Two involutions $\backslash theta\_1$ and $\backslash theta\_2$ are considered equivalent if they differ only by an inner automorphism. Any real semisimple Lie algebra has a Cartan involution, and any two Cartan involutions are equivalent. 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「Cartan decomposition」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.