翻訳と辞書 Words near each other ・ Quashquame ・ Quasi ・ Quasi alliance ・ Quasi at the Quackadero ・ Quasi corporation ・ Quasi Delay Insensitive ・ Quasi Fermi level ・ Quasi in rem jurisdiction ・ Quasi Object ・ Quasi Self Boot 93–96 ・ Quasi Universal Intergalactic Denomination ・ Quasi-algebraically closed field ・ Quasi-analog signal ・ Quasi-analytic function ・ Quasi-arithmetic mean ・ Quasi-bialgebra ・ Quasi-biennial oscillation ・ Quasi-bipartite graph ・ Quasi-birth–death process ・ Quasi-category ・ Quasi-commutative property ・ Quasi-compact morphism ・ Quasi-constitutionality ・ Quasi-continuous function ・ Quasi-contract ・ Quasi-criminal ・ Quasi-crystals (supramolecular) ・ Quasi-delict ・ Quasi-derivative ・ Quasi-elemental 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-bialgebra ： ウィキペディア英語版 Quasi-bialgebra In mathematics, quasi-bialgebras are a generalization of bialgebras: they were first defined by the Ukrainian mathematician Vladimir Drinfeld in 1990. A quasi-bialgebra differs from a bialgebra by having coassociativity replaced by an invertible element $\backslash Phi$ which controls the non-coassociativity. One of their key properties is that the corresponding category of modules forms a tensor category. == Definition == A quasi-bialgebra $\backslash mathcal\; =\; (\backslash mathcal,\; \backslash Delta,\; \backslash varepsilon,\; \backslash Phi,l,r)$ is an algebra $\backslash mathcal$ over a field $\backslash mathbb$ equipped with morphisms of algebras :$\backslash Delta\; :\; \backslash mathcal\; \backslash rightarrow\; \backslash mathcal$ :$\backslash varepsilon\; :\; \backslash mathcal\; \backslash rightarrow\; \backslash mathbb$ along with invertible elements $\backslash Phi\; \backslash in\; \backslash mathcal$, and $r,l\; \backslash in\; A$ such that the following identities hold: :$(id\; \backslash otimes\; \backslash Delta)\; \backslash circ\; \backslash Delta(a)\; =\; \backslash Phi\; \backslash lbrack\; (\backslash Delta\; \backslash otimes\; id)\; \backslash circ\; \backslash Delta\; (a)\; \backslash rbrack\; \backslash Phi^,\; \backslash quad\; \backslash forall\; a\; \backslash in\; \backslash mathcal$ :$\backslash lbrack\; (id\; \backslash otimes\; id\; \backslash otimes\; \backslash Delta)(\backslash Phi)\; \backslash rbrack\; \backslash \; \backslash lbrack\; (\backslash Delta\; \backslash otimes\; id\; \backslash otimes\; id)(\backslash Phi)\; \backslash rbrack\; =\; (1\; \backslash otimes\; \backslash Phi)\; \backslash \; \backslash lbrack\; (id\; \backslash otimes\; \backslash Delta\; \backslash otimes\; id)(\backslash Phi)\; \backslash rbrack\; \backslash \; (\backslash Phi\; \backslash otimes\; 1)$ :$(\backslash varepsilon\; \backslash otimes\; id)(\backslash Delta\; a)\; =\; l^\; a\; l,\; \backslash qquad\; (id\; \backslash otimes\; \backslash varepsilon)\; \backslash circ\; \backslash Delta\; =\; r^\; a\; r,\; \backslash quad\; \backslash forall\; a\; \backslash in\; \backslash mathcal$ :$(id\; \backslash otimes\; \backslash varepsilon\; \backslash otimes\; id)(\backslash Phi)\; =\; 1\; \backslash otimes\; 1.$ Where $\backslash Delta$ and $\backslash epsilon$ are called the comultiplication and counit, $r$ and $l$ are called the right and left unit constraints (resp.), and $\backslash Phi$ is sometimes called the ''Drinfeld associator''.〔C. Kassel. "Quantum Groups". Graduate Texts in Mathematics Springer-Verlag. ISBN 0387943706〕 This definition is constructed so that the category $\backslash mathcal-Mod$ is a tensor category under the usual vector space tensor product, and in fact this can be taken as the definition instead of the list of above identities.〔 Since many of the quasi-bialgebras that appear "in nature" have trivial unit constraints, ie. $l=r=1$ the definition may sometimes be given with this assumed.〔 Note that a bialgebra is just a quasi-bialgebra with trivial unit and associativity constraints: $l=r=1$ and $\backslash Phi=1\; \backslash otimes\; 1\; \backslash otimes\; 1$. 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-bialgebra」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.