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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 Adjoint bundle ： ウィキペディア英語版 Adjoint bundle In mathematics, an adjoint bundle 〔 (page 96 )〕 〔 page 161 and page 400 〕 is a vector bundle naturally associated to any principal bundle. The fibers of the adjoint bundle carry a Lie algebra structure making the adjoint bundle into a (nonassociative) algebra bundle. Adjoint bundles have important applications in the theory of connections as well as in gauge theory. ==Formal definition== Let ''G'' be a Lie group with Lie algebra $\backslash mathfrak\; g$, and let ''P'' be a principal ''G''-bundle over a smooth manifold ''M''. Let :$\backslash mathrm:\; G\backslash to\backslash mathrm(\backslash mathfrak\; g)\backslash sub\backslash mathrm(\backslash mathfrak\; g)$ be the adjoint representation of ''G''. The adjoint bundle of ''P'' is the associated bundle :$\backslash mathrm\; P\; =\; P\backslash times^\_\_\{g^\{-1\}\}(x)">)$ for all ''g'' ∈ ''G''. Since the structure group of the adjoint bundle consists of Lie algebra automorphisms, the fibers naturally carry a Lie algebra structure making the adjoint bundle into a bundle of Lie algebras over ''M''. 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「Adjoint bundle」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.