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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 Harish-Chandra isomorphism ： ウィキペディア英語版 Harish-Chandra isomorphism In mathematics, the Harish-Chandra isomorphism, introduced by , is an isomorphism of commutative rings constructed in the theory of Lie algebras. The isomorphism maps the center ''Z''(''U''(''g'')) of the universal enveloping algebra ''U''(''g'') of a reductive Lie algebra ''g'' to the elements ''S''(''h'')''W'' of the symmetric algebra ''S''(''h'') of a Cartan subalgebra ''h'' that are invariant under the Weyl group ''W''. ==Fundamental invariants== Let ''n'' be the rank of ''g'', which is the dimension of the Cartan subalgebra ''h''. H. S. M. Coxeter observed that ''S''(''h'')''W'' is a polynomial algebra in ''n'' variables (see Chevalley–Shephard–Todd theorem for a more general statement). Therefore, the center of the universal enveloping algebra of a reductive Lie algebra is a polynomial algebra. The degrees of the generators are the degrees of the fundamental invariants given in the following table. For example, the center of the universal enveloping algebra of ''G''2 is a polynomial algebra on generators of degrees 2 and 6. 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「Harish-Chandra isomorphism」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.