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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 Ribbon Hopf algebra ： ウィキペディア英語版 Ribbon Hopf algebra A ribbon Hopf algebra $(A,m,\backslash Delta,u,\backslash varepsilon,S,\backslash mathcal,\backslash nu)$ is a quasitriangular Hopf algebra which possess an invertible central element $\backslash nu$ more commonly known as the ribbon element, such that the following conditions hold: :$\backslash nu^=uS(u),\; \backslash ;\; S(\backslash nu)=\backslash nu,\; \backslash ;\; \backslash varepsilon\; (\backslash nu)=1$ :$\backslash Delta\; (\backslash nu)=(\backslash mathcal\_\backslash mathcal\_)^(\backslash nu\; \backslash otimes\; \backslash nu\; )$ where $u=m(S\backslash otimes\; \backslash text)(\backslash mathcal\_)$. Note that the element ''u'' exists for any quasitriangular Hopf algebra, and $uS(u)$ must always be central and satisfies $S(uS(u))=uS(u),\; \backslash varepsilon(uS(u))=1,\; \backslash Delta(uS(u))\; =$ (\mathcal_\mathcal_)^(uS(u) \otimes uS(u)), so that all that is required is that it have a central square root with the above properties. Here :$A$ is a vector space :$m$ is the multiplication map $m:A\; \backslash otimes\; A\; \backslash rightarrow\; A$ :$\backslash Delta$ is the co-product map $\backslash Delta:\; A\; \backslash rightarrow\; A\; \backslash otimes\; A$ :$u$ is the unit operator $u:\backslash mathbb\; \backslash rightarrow\; A$ :$\backslash varepsilon$ is the co-unit operator $\backslash varepsilon:\; A\; \backslash rightarrow\; \backslash mathbb$ :$S$ is the antipode $S:\; A\backslash rightarrow\; A$ :$\backslash mathcal$ is a universal R matrix We assume that the underlying field $K$ is $\backslash mathbb$ == See also == *Quasitriangular Hopf algebra *Quasi-triangular quasi-Hopf 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「Ribbon Hopf 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.