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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 Loop algebra ： ウィキペディア英語版 Loop algebra In mathematics, loop algebras are certain types of Lie algebras, of particular interest in theoretical physics. ==Definition== If is a Lie algebra, the tensor product of with , the algebra of (complex) smooth functions over the circle manifold , :$\backslash mathfrak\backslash otimes\; C^\backslash infty(S^1)$, is an infinite-dimensional Lie algebra with the Lie bracket given by :$(f\_1,g\_2\; \backslash otimes\; f\_2)=()\backslash otimes\; f\_1\; f\_2$. Here and are elements of and and are elements of . This isn't precisely what would correspond to the direct product of infinitely many copies of , one for each point in , because of the smoothness restriction. Instead, it can be thought of in terms of smooth map from to ; a smooth parametrized loop in , in other words. This is why it is called the loop algebra. 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「Loop 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.