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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 Hurwitz quaternion order ： ウィキペディア英語版 Hurwitz quaternion order The Hurwitz quaternion order is a specific order in a quaternion algebra over a suitable number field. The order is of particular importance in Riemann surface theory, in connection with surfaces with maximal symmetry, namely the Hurwitz surfaces.〔.〕 The Hurwitz quaternion order was studied in 1967 by Goro Shimura,〔.〕 but first explicitly described by Noam Elkies in 1998.〔.〕 For an alternative use of the term, see Hurwitz quaternion (both usages are current in the literature). ==Definition== Let $K$ be the maximal real subfield of $\backslash mathbb$$(\backslash rho)$ where $\backslash rho$ is a 7th-primitive root of unity. The ring of integers of $K$ is $\backslash mathbb()$, where the element $\backslash eta=\backslash rho+\; \backslash bar\backslash rho$ can be identified with the positive real $2\backslash cos(\backslash tfrac)$. Let $D$ be the quaternion algebra, or symbol algebra :$D:=\backslash ,(\backslash eta,\backslash eta)\_,$ so that $i^2=j^2=\backslash eta$ and $ij=-ji$ in $D.$ Also let $\backslash tau=1+\backslash eta+\backslash eta^2$ and $j\text{'}=\backslash tfrac(1+\backslash eta\; i\; +\; \backslash tau\; j)$. Let :$\backslash mathcal\_()().$ Then $\backslash mathcal\_\{\backslash mathrm\{Hur\}\}$ is a maximal order of $D$, described explicitly by Noam Elkies.〔.〕 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「Hurwitz quaternion order」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.