翻訳と辞書 Words near each other ・ Braid My Hair ・ Braid Station ・ Braid statistics ・ Braid theory ・ Braid-breaker ・ Braided ・ Braided cheese ・ Braided fishing line ・ Braided Hopf algebra ・ Braided monoidal category ・ Braided Path ・ Braided river ・ Braided River (Publishing) ・ Braided rug ・ Braided stainless steel brake lines ・ Braided vector space ・ Braidfauld ・ Braidhurst High School ・ Braiding machine ・ Braidley ・ Braids (band) ・ Braids on a Bald Head ・ Braidwood ・ Braidwood (surname) ・ Braidwood Inquiry ・ Braidwood Nuclear Generating Station ・ Braidwood, Illinois ・ Braidwood, New South Wales ・ Braidwood, South Lanarkshire ・ Braies 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 Braided vector space ： ウィキペディア英語版 Braided vector space In mathematics, a braided vectorspace $\backslash ;V$ is a vector space together with an additional structure map $\backslash tau\backslash ;$ symbolizing interchanging of two vector tensor copies: ::$\backslash tau:\backslash ;\; V\backslash otimes\; V\backslash longrightarrow\; V\backslash otimes\; V\; \backslash ,$ such that the Yang–Baxter equation is fulfilled. Hence drawing tensor diagrams with $\backslash tau\backslash ;$ an overcrossing the corresponding composed morphism is unchanged when a Reidemeister move is applied to the tensor diagram and thus they present a representation of the braid group. As first example, every vector space is braided via the trivial braiding (simply flipping). A superspace has a braiding with negative sign in braiding two odd vectors. More generally, a diagonal braiding means that for a $\backslash ;V$-base $x\_i\backslash ;$ we have ::$\backslash tau(x\_i\backslash otimes\; x\_j)=q\_(x\_j\backslash otimes\; x\_i)\; \backslash ,$ A good source for braided vector spaces entire braided monoidal categories with braidings between any objects $\backslash tau\_\backslash ;$, most importantly the modules over quasitriangular Hopf algebras and Yetter–Drinfeld modules over finite groups (such as $\backslash mathbb\_2$ above) If $V\backslash ;$ additionally possesses an algebra structure inside the braided category ("braided algebra") one has a braided commutator (e.g. for a superspace the anticommutator): ::$\backslash ;()\_\backslash tau:=\backslash mu((x\backslash otimes\; y)-\backslash tau(x\backslash otimes\; y))\backslash qquad\; \backslash mu(x\backslash otimes\; y):=xy$ Examples of such braided algebras (and even Hopf algebras) are the Nichols algebras, that are by definition generated by a given braided vectorspace. They appear as quantum Borel part of quantum groups and often (e.g. when finite or over an abelian group) possess an arithmetic root system, multiple Dynkin diagrams and a PBW-basis made up of braided commutators just like the ones in semisimple Lie algebras. 〔Andruskiewitsch, Schneider: ''Pointed Hopf algebras'', New directions in Hopf algebras, 1–68, Math. Sci. Res. Inst. Publ., 43, Cambridge Univ. Press, Cambridge, 2002.〕 〔 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 vector space」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.