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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 Glennie's identity ： ウィキペディア英語版 Glennie's identity In mathematics, Glennie's identity is an identity used by Charles M. Glennie to establish some s-identities that are valid in special Jordan algebras but not in all Jordan algebras. A Jordan s-identity ("s" for special) is a Jordan polynomial〔In this context, Jordan polynomial is a polynomial operator on a Jordan algebra. The Jordan algebra is named after Pascual Jordan and not the Camille Jordan famous for the Jordan normal form. Jordan polynomial has a different meaning in the context of the Jordan normal form.〕 which vanishes in all special Jordan algebras but not in all Jordan algebras. What is now known as Glennie's identity first appeared in his 1963 Yale PhD thesis with Nathan Jacobson as thesis advisor. ==Formal definition== Let • denote the product in a special Jordan algebra $A$. For all ''X'', ''Y'', ''Z'' in ''A'', define the Jordan triple product # = (''X''•''Y'')•''Z'' − (''Y''•''Z'')•''X'' + (''Z''•''X'')•''Y'' then Glennie's identity ''G''8 holds in the form: #2, ''Y'', ''Z''•''X''} − , ''Z''} = 2 } − , ''X''}. 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「Glennie's 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.