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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 Chevalley basis ： ウィキペディア英語版 Chevalley basis In mathematics, a Chevalley basis for a simple complex Lie algebra is a basis constructed by Claude Chevalley with the property that all structure constants are integers. Chevalley used these bases to construct analogues of Lie groups over finite fields, called Chevalley groups. The generators of a Lie group are split into the generators ''H'' and ''E'' indexed by simple roots and their negatives $\backslash pm\backslash alpha\_i$. The relations among the generators are the following: :$()=0$ :$()=\backslash alpha\_j(H\_)\; E\_$ :$()\; =\; H\_$ :$()=\backslash pm(p+1)E\_$ where in the last relation $p$ is the greatest positive integer such that $\backslash gamma\; -p\backslash beta$ is a root and we consider $E\_\; =\; 0$ if $\backslash beta\; +\; \backslash gamma$ is not a root. For determining the sign in the last relation one fixes an ordering of roots which respects addition, i.e., if $\backslash beta\; \backslash prec\; \backslash gamma$ then $\backslash beta\; +\; \backslash alpha\; \backslash prec\; \backslash gamma\; +\; \backslash alpha$ provided that all four are roots. We then call $(\backslash beta,\; \backslash gamma)$ an extraspecial pair of roots if they are both positive and $\backslash beta$ is minimal among all $\backslash beta\_0$ that occur in pairs of positive roots $(\backslash beta\_0,\; \backslash gamma\_0)$ satisfying $\backslash beta\_0\; +\; \backslash gamma\_0\; =\; \backslash beta\; +\; \backslash gamma$. The sign in the last relation can be chosen arbitrarily whenever $(\backslash beta,\; \backslash gamma)$ is an extraspecial pair of roots. This then determines the signs for all remaining pairs of roots. ==References== *''Simple Groups of Lie Type'' by Roger W. Carter, ISBN 0-471-50683-4 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「Chevalley basis」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.