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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 Cyclotomic identity ： ウィキペディア英語版 Cyclotomic identity In mathematics, the cyclotomic identity states that :$=\backslash prod\_^\backslash infty\backslash left(\backslash right)^$ where ''M'' is Moreau's necklace-counting function, :$M(\backslash alpha,n)=\backslash sum\_\backslash mu\backslash left(\backslash right)\backslash alpha^d,$ and ''μ'' is the classic Möbius function of number theory. The name comes from the denominator, 1 − ''z'' ''j'', which is the product of cyclotomic polynomials. The left hand side of the cyclotomic identity is the generating function for the free associative algebra on α generators, and the right hand side is the generating function for the universal enveloping algebra of the free Lie algebra on α generators. The cyclotomic identity witnesses the fact that these two algebras are isomorphic. There is also a symmetric generalization of the cyclotomic identity found by Strehl: :$\backslash prod\_^\backslash infty\backslash left(\backslash right)^=\backslash prod\_^\backslash infty\backslash left(\backslash right)^$ ==References== * 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「Cyclotomic identity」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.