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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Lawrence–Krammer representation ： ウィキペディア英語版 Lawrence–Krammer representation In mathematics the Lawrence–Krammer representation is a representation of the braid groups. It fits into a family of representations called the Lawrence representations. The 1st Lawrence representation is the Burau representation and the 2nd is the Lawrence–Krammer representation. The Lawrence–Krammer representation is named after Ruth Lawrence and Daan Krammer. == Definition == Consider the braid group $B\_n$ to be the mapping class group of a disc with ''n'' marked points $P\_n$. The Lawrence–Krammer representation is defined as the action of $B\_n$ on the homology of a certain covering space of the configuration space $C\_2\; P\_n$. Specifically, $H\_1\; C\_2\; P\_n\; \backslash simeq\; \backslash mathbb\; Z^$, and the subspace of $H\_1\; C\_2\; P\_n$ invariant under the action of $B\_n$ is primitive, free and of rank 2. Generators for this invariant subspace are denoted by $q,\; t$. The covering space of $C\_2\; P\_n$ corresponding to the kernel of the projection map :$\backslash pi\_1\; C\_2\; P\_n\; \backslash to\; \backslash mathbb\; Z^2\; \backslash langle\; q,t\; \backslash rangle$ is called the Lawrence–Krammer cover and is denoted $\backslash overline$. Diffeomorphisms of$P\_n$ act on $P\_n$, thus also on $C\_2\; P\_n$, moreover they lift uniquely to diffeomorphisms of $\backslash overline$ which restrict to identity on the co-dimension two boundary stratum (where both points are on the boundary circle). The action of $B\_n$ on :$H\_2\; \backslash overline,$ thought of as a :$\backslash mathbb\; Z\backslash langle\; t^,q^\backslash rangle$-module, is the Lawrence–Krammer representation. $H\_2\; \backslash overline$ is known to be a free $\backslash mathbb\; Z\backslash langle\; t^,q^\backslash rangle$-module, of rank $n\; \backslash choose\; 2$. 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「Lawrence–Krammer representation」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.