翻訳と辞書 Words near each other ・ Quasi-property ・ Quasi-quotation ・ Quasi-realism ・ Quasi-reflexive ・ Quasi-relative interior ・ Quasi-rent ・ Quasi-satellite ・ Quasi-separated morphism ・ Quasi-set theory ・ Quasi-solid ・ Quasi-split group ・ Quasi-star ・ Quasi-syllogism ・ Quasi-synchronous transmission ・ Quasi-tort ・ Quasi-triangular quasi-Hopf algebra ・ Quasi-triangulation ・ Quasi-War ・ Quasi-Zenith Satellite System ・ Quasianosteosaurus ・ Quasiatom ・ Quasicaecilia ・ Quasicircle ・ Quasiconcha ・ Quasiconformal mapping ・ Quasicontraction semigroup ・ Quasiconus ・ Quasiconvex function ・ Quasicooronga ・ Quasicravenoceras Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Quasi-triangular quasi-Hopf algebra ： ウィキペディア英語版 Quasi-triangular quasi-Hopf algebra A quasi-triangular quasi-Hopf algebra is a specialized form of a quasi-Hopf algebra defined by the Ukrainian mathematician Vladimir Drinfeld in 1989. It is also a generalized form of a quasi-triangular Hopf algebra. A quasi-triangular quasi-Hopf algebra is a set $\backslash mathcal\; =\; (\backslash mathcal,\; R,\; \backslash Delta,\; \backslash varepsilon,\; \backslash Phi)$ where $\backslash mathcal\; =\; (\backslash mathcal,\; \backslash Delta,\; \backslash varepsilon,\; \backslash Phi)$ is a quasi-Hopf algebra and $R\; \backslash in\; \backslash mathcal$ known as the R-matrix, is an invertible element such that :$R\; \backslash Delta(a)\; =\; \backslash sigma\; \backslash circ\; \backslash Delta(a)\; R,\; a\; \backslash in\; \backslash mathcal$ :$\backslash sigma:\; \backslash mathcal\; \backslash rightarrow\; \backslash mathcal$ :$x\; \backslash otimes\; y\; \backslash rightarrow\; y\; \backslash otimes\; x$ so that $\backslash sigma$ is the switch map and :$(\backslash Delta\; \backslash otimes\; \backslash operatorname)R\; =\; \backslash Phi\_R\_\backslash Phi\_^R\_\backslash Phi\_$ :$(\backslash operatorname\; \backslash otimes\; \backslash Delta)R\; =\; \backslash Phi\_^R\_\backslash Phi\_R\_\backslash Phi\_^$ where $\backslash Phi\_\; =\; x\_a\; \backslash otimes\; x\_b\; \backslash otimes\; x\_c$ and $\backslash Phi\_=\; \backslash Phi\; =\; x\_1\; \backslash otimes\; x\_2\; \backslash otimes\; x\_3\; \backslash in\; \backslash mathcal$. The quasi-Hopf algebra becomes ''triangular'' if in addition, $R\_R\_=1$. The twisting of $\backslash mathcal$ by $F\; \backslash in\; \backslash mathcal$ is the same as for a quasi-Hopf algebra, with the additional definition of the twisted ''R''-matrix A quasi-triangular (resp. triangular) quasi-Hopf algebra with $\backslash Phi=1$ is a quasi-triangular (resp. triangular) Hopf algebra as the latter two conditions in the definition reduce the conditions of quasi-triangularity of a Hopf algebra . Similarly to the twisting properties of the quasi-Hopf algebra, the property of being quasi-triangular or triangular quasi-Hopf algebra is preserved by twisting. == See also == *Ribbon 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「Quasi-triangular quasi-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.