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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 Braided Hopf algebra ： ウィキペディア英語版 Braided Hopf algebra In mathematics, a braided Hopf algebra is a Hopf algebra in a braided monoidal category. The most common braided Hopf algebras are objects in a Yetter–Drinfeld category of a Hopf algebra ''H'', particurlarly the Nichols algebra of a braided vectorspace in that category. ''The notion should not be confused with quasitriangular Hopf algebra.'' == Definition == Let ''H'' be a Hopf algebra over a field ''k'', and assume that the antipode of ''H'' is bijective. A Yetter–Drinfeld module ''R'' over ''H'' is called a braided bialgebra in the Yetter–Drinfeld category $^H\_H\backslash mathcal$, where the algebra structure of $R\backslash otimes\; R$ is determined by the unit $\backslash eta\; \backslash otimes\; \backslash eta(1)\; :\; k\backslash to\; R\backslash otimes\; R$ and the multiplication map :: $(R\backslash otimes\; R)\backslash times\; (R\backslash otimes\; R)\backslash to\; R\backslash otimes\; R,\backslash quad\; (r\backslash otimes\; s,t\backslash otimes\; u)\; \backslash mapsto\; \backslash sum\; \_i\; rt\_i\backslash otimes\; s\_i\; u,\; \backslash quad\; \backslash text\backslash quad\; c(s\backslash otimes\; t)=\backslash sum\; \_i\; t\_i\backslash otimes\; s\_i.$ :Here ''c'' is the canonical braiding in the Yetter–Drinfeld category $^H\_H\backslash mathcal$ is called a braided Hopf algebra, if there is a morphism $S:R\backslash to\; R$ of Yetter–Drinfeld modules such that :: $S(r^)r^=r^S(r^)=\backslash eta(\backslash varepsilon\; (r))$ for all $r\backslash in\; R,$ where $\backslash Delta\; \_R(r)=r^\backslash otimes\; r^$ in slightly modified Sweedler notation – a change of notation is performed in order to avoid confusion in Radford's biproduct below. 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「Braided 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.