翻訳と辞書 Words near each other ・ Artime ・ Artimes Farshad Yeganeh ・ Artimet ・ ARTIMIS ・ Artimus Parker ・ Artimus Pyle ・ Artin ・ Artin (name) ・ Artin algebra ・ Artin approximation theorem ・ Artin billiard ・ Artin Boşgezenyan ・ Artin conductor ・ Artin conjecture ・ Artin Dadyan Pasha ・ Artin group ・ Artin Hindoğlu ・ Artin Jelow ・ Artin L-function ・ Artin Madoyan ・ Artin Penik ・ Artin Poturlyan ・ Artin reciprocity law ・ Artin transfer (group theory) ・ Artin's conjecture on primitive roots ・ Artine Artinian ・ Artines ・ Artington ・ Artinian ・ Artinian ideal 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 Artin group ： ウィキペディア英語版 Artin group In mathematics, an Artin group (or generalized braid group) is a group with a presentation of the form :$\backslash Big\backslash langle\; x\_1,x\_2,\backslash ldots,x\_n\; \backslash Big|\; \backslash langle\; x\_1,\; x\_2\; \backslash rangle^\},\; \backslash ldots\; ,\; \backslash langle\; x\_,\; x\_n\; \backslash rangle^,\; x\_\; \backslash rangle^\; =\; m\_\; \backslash in\; \backslash$. For , $\backslash langle\; x\_i,\; x\_j\; \backslash rangle^m$ denotes an alternating product of $x\_i$ and $x\_j$ of length $m$, beginning with $x\_i$. For example, :$\backslash langle\; x\_i,\; x\_j\; \backslash rangle^3\; =\; x\_ix\_jx\_i$ and :$\backslash langle\; x\_i,\; x\_j\; \backslash rangle^4\; =\; x\_ix\_jx\_ix\_j$. If $m=\backslash infty$, then there is (by convention) no relation for $x\_i$ and $x\_j$. The integers $m\_$ can be organized into a symmetric matrix, known as the Coxeter matrix of the group. Each Artin group has as a quotient the Coxeter group with the same set of generators and Coxeter matrix. The kernel of the homomorphism to the associated Coxeter group, known as the pure Artin group, is generated by relations of the form $^2=1$. == Classes of Artin groups == Braid groups are examples of Artin groups, with Coxeter matrix $m\_\; =\; 3$ and $m\_=2$ for $|i-j|>1.$ Several important classes of Artin groups can be defined in terms of the properties of the Coxeter matrix. 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「Artin group」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.