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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 , :, is an infinite-dimensional Lie algebra with the Lie bracket given by :. 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
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