翻訳と辞書 Words near each other ・ Quasi-elemental ・ Quasi-empirical method ・ Quasi-empiricism in mathematics ・ Quasi-experiment ・ Quasi-fibration ・ Quasi-finite field ・ Quasi-finite morphism ・ Quasi-foreign corporation ・ Quasi-Frobenius Lie algebra ・ Quasi-Frobenius ring ・ Quasi-Fuchsian group ・ Quasi-geostrophic equations ・ Quasi-harmonic approximation ・ Quasi-Hilda comet ・ Quasi-homogeneous polynomial ・ Quasi-Hopf algebra ・ Quasi-identifier ・ Quasi-invariant measure ・ Quasi-irreversible inhibitor ・ Quasi-isometry ・ Quasi-isomorphism ・ Quasi-judicial body ・ Quasi-judicial proceedings ・ Quasi-legislative capacity ・ Quasi-Lie algebra ・ Quasi-likelihood ・ Quasi-linkage equilibrium ・ Quasi-market ・ Quasi-maximum likelihood ・ Quasi-median networks 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-Hopf algebra ： ウィキペディア英語版 Quasi-Hopf algebra A quasi-Hopf algebra is a generalization of a Hopf algebra, which was defined by the Russian mathematician Vladimir Drinfeld in 1989. A ''quasi-Hopf algebra'' is a quasi-bialgebra $\backslash mathcal\; =\; (\backslash mathcal,\; \backslash Delta,\; \backslash varepsilon,\; \backslash Phi)$ for which there exist $\backslash alpha,\; \backslash beta\; \backslash in\; \backslash mathcal$ and a bijective antihomomorphism ''S'' (antipode) of $\backslash mathcal$ such that : $\backslash sum\_i\; S(b\_i)\; \backslash alpha\; c\_i\; =\; \backslash varepsilon(a)\; \backslash alpha$ : $\backslash sum\_i\; b\_i\; \backslash beta\; S(c\_i)\; =\; \backslash varepsilon(a)\; \backslash beta$ for all $a\; \backslash in\; \backslash mathcal$ and where :$\backslash Delta(a)\; =\; \backslash sum\_i\; b\_i\; \backslash otimes\; c\_i$ and :$\backslash sum\_i\; X\_i\; \backslash beta\; S(Y\_i)\; \backslash alpha\; Z\_i\; =\; \backslash mathbb,$ :$\backslash sum\_j\; S(P\_j)\; \backslash alpha\; Q\_j\; \backslash beta\; S(R\_j)\; =\; \backslash mathbb.$ where the expansions for the quantities $\backslash Phi$and $\backslash Phi^$ are given by :$\backslash Phi\; =\; \backslash sum\_i\; X\_i\; \backslash otimes\; Y\_i\; \backslash otimes\; Z\_i$ and :$\backslash Phi^=\; \backslash sum\_j\; P\_j\; \backslash otimes\; Q\_j\; \backslash otimes\; R\_j.$ As for a quasi-bialgebra, the property of being quasi-Hopf is preserved under twisting. == Usage == Quasi-Hopf algebras form the basis of the study of Drinfeld twists and the representations in terms of F-matrices associated with finite-dimensional irreducible representations of quantum affine algebra. F-matrices can be used to factorize the corresponding R-matrix. This leads to applications in Statistical mechanics, as quantum affine algebras, and their representations give rise to solutions of the Yang-Baxter equation, a solvability condition for various statistical models, allowing characteristics of the model to be deduced from its corresponding quantum affine algebra. The study of F-matrices has been applied to models such as the Heisenberg XXZ model in the framework of the algebraic Bethe ansatz. It provides a framework for solving two-dimensional integrable models by using the Quantum inverse scattering method. 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-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.