翻訳と辞書 Words near each other ・ Birlik, Kazakhstan ・ Birling ・ Birling, Kent ・ Birling, Northumberland ・ Birlingham ・ Birlinn ・ Birlinn (publisher) ・ Birmabright ・ Birmaharajpur ・ Birmaharajpur (Odisha Vidhan Sabha constituency) ・ Birmaharajpur College ・ Birman ・ Birman (surname) ・ Birmania Ríos ・ Birmanites ・ Birman–Wenzl algebra ・ Birmensdorf railway station ・ Birmensdorf, Zürich ・ Birmenstorf, Aargau ・ Birmenstorf, Switzerland ・ Birmingham ・ Birmingham & District Amateur Football Association ・ Birmingham & Solihull R.F.C. ・ Birmingham (Amanda Marshall song) ・ Birmingham (crater) ・ Birmingham (disambiguation) ・ Birmingham (horse) ・ Birmingham (Live with Orchestra & Choir) ・ Birmingham (surname) ・ Birmingham (UK Parliament constituency) 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 Birman–Wenzl algebra ： ウィキペディア英語版 Birman–Wenzl algebra In mathematics, the Birman-Murakami-Wenzl (BMW) algebra, introduced by and , is a two-parameter family of algebras C''n''(''ℓ'', ''m'') of dimension 1·3·5 ··· (2''n'' − 1) having the Hecke algebra of the symmetric group as a quotient. It is related to the Kauffman polynomial of a link. It is a deformation of the Brauer algebra in much the same way that Hecke algebras are deformations of the group algebra of the symmetric group. ==Definition== For each natural number ''n'', the BMW algebra C''n''(''ℓ'', ''m'') is generated by G''1'',G''2'',...,G''n-1'',E''1'',E''2'',...,E''n-1'' and relations: :$G\_iG\_j=G\_jG\_i,\; \backslash mathrm\; \backslash left\backslash vert\; i-j\; \backslash right\backslash vert\; \backslash geqslant\; 2,$ :$G\_i\; G\_\; G\_i=G\_\; G\_i\; G\_,$         $E\_i\; E\_\; E\_i=E\_i,$ :$G\_i\; +\; ^=m(1+E\_i),$ :$G\_\; G\_i\; E\_\; =\; E\_i\; G\_\; G\_i\; =\; E\_i\; E\_,$      $G\_\; E\_i\; G\_\; =^\; E\_\; ^,$ :$G\_\; E\_i\; E\_=^\; E\_,$      $E\_\; E\_i\; G\_\; =E\_\; ^,$ :$G\_i\; E\_i=\; E\_i\; G\_i\; =\; l^\; E\_i,$     $E\_i\; G\_\; E\_i\; =l\; E\_i.$ These relations imply the further relations: :$E\_i\; E\_j=E\_j\; E\_i,\; \backslash mathrm\; \backslash left\backslash vert\; i-j\; \backslash right\backslash vert\; \backslash geqslant\; 2,$ :$(E\_i)^2\; =\; (m^(l+l^)-1)\; E\_i,\; \backslash ,\backslash !$ :$^2\; =\; m(G\_i+l^E\_i)-1.$ This is the original definition given by Birman & Wenzl. However a slight change by the introduction of some minus signs is sometimes made, in accordance with Kauffman's 'Dubrovnik' version of his link invariant. In that way, the fourth relation in Birman & Wenzl's original version is changed to (1) (Kauffman skein relation) ::$G\_i\; -\; ^=m(1-E\_i),$ :Given invertibility of ''m'', the rest of the relations in Birman & Wenzl's original version can be reduced to (2) (Idempotent relation) ::$(E\_i)^2\; =\; (m^(l-l^)+1)\; E\_i,\; \backslash ,\backslash !$ (3) (Braid relations) ::$G\_iG\_j=G\_jG\_i,\; \backslash text\; \backslash left\backslash vert\; i-j\; \backslash right\backslash vert\; \backslash geqslant\; 2,\; \backslash text\; G\_i\; G\_\; G\_i=G\_\; G\_i\; G\_,\; \backslash ,\backslash !$ (4) (Tangle relations) ::$E\_i\; E\_\; E\_i=E\_i\; \backslash text\; G\_i\; G\_\; E\_i\; =\; E\_\; E\_i,$ (5) (Delooping relations) ::$G\_i\; E\_i=\; E\_i\; G\_i\; =\; l^\; E\_i\; \backslash text\; E\_i\; G\_\; E\_i\; =l\; E\_i.$ 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「Birman–Wenzl 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.