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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 Lie conformal algebra ： ウィキペディア英語版 Lie conformal algebra A Lie conformal algebra is in some sense a generalization of a Lie algebra in that it too is a "Lie algebra," though in a different pseudo-tensor category. Lie conformal algebras are very closely related to vertex algebras and have many applications in other areas of algebra and integrable systems. ==Definition and relation to Lie algebras== A Lie algebra is defined to be a vector space with a skew symmetric bilinear multiplication which satisfies the Jacobi identity. More generally, a Lie algebra is an object, $L$ in the category of vector spaces (read: $\backslash mathbb$-modules) with a morphism :$():L\backslash otimes\; L\backslash rightarrow\; L$ that is skew-symmetric and satisfies the Jacobi identity. A Lie conformal algebra, then, is an object $R$ in the category of $\backslash mathbb()$-modules with morphism :$():R\backslash otimes\; R\backslash rightarrow\backslash mathbb()\backslash otimes\; R$ called the lambda bracket, which satisfies modified versions of bilinearity, skew-symmetry and the Jacobi identity: :$(a\_\backslash lambda\; b)=-\backslash lambda(b),\; (\backslash partial\; b)\; =\; (\backslash lambda\; +\; \backslash partial)(b),$ :$(b)=-(),\; \backslash ,$ :$]=(b)\_c].\; \backslash ,$ One can see that "removing all the lambda's, mu's and partials from the brackets, one simply has the definition of a Lie 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「Lie conformal 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.