翻訳と辞書 Words near each other ・ Connectify ・ Connectify Hotspot ・ Connecting Futures ・ Connecting Link ・ Connecting Railway ・ COnnecting REpositories ・ Connecting rod ・ Connecting Rooms ・ Connecting Slough ・ Connecting Spirits ・ Connecting stalk ・ Connecting tubule ・ Connection ・ Connection (affine bundle) ・ Connection (album) ・ Connection (algebraic framework) ・ Connection (composite bundle) ・ Connection (dance) ・ Connection (Don Ellis album) ・ Connection (Elastica song) ・ Connection (EP) ・ Connection (fibred manifold) ・ Connection (mathematics) ・ Connection (principal bundle) ・ Connection (The Rolling Stones song) ・ Connection (vector bundle) ・ Connection broker ・ Connection Collection, Vol. 1 ・ Connection Distributing Co. v. Holder ・ Connection form Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Connection (algebraic framework) ： ウィキペディア英語版 Connection (algebraic framework) Geometry of quantum systems (e.g., noncommutative geometry and supergeometry) is mainly phrased in algebraic terms of modules and algebras. Connections on modules are generalization of a linear connection on a smooth vector bundle $E\backslash to$ X written as a Koszul connection on the $C^\backslash infty(X)$-module of sections of $E\backslash to$ X.〔Koszul (1950)〕 == Commutative algebra == Let $A$ be a commutative ring and $P$ a $A$-module. There are different equivalent definitions of a connection on $P$.〔Koszul (1950), Mangiarotti (2000)〕 Let $D(A)$ be the module of derivations of a ring $A$. A connection on an $A$-module $P$ is defined as an $A$-module morphism : $\backslash nabla:D(A)\backslash ni\; u\backslash to\; \backslash nabla\_u\backslash in\; \backslash mathrm\_1(P,P)$ such that the first order differential operators $\backslash nabla\_u$ on $P$ obey the Leibniz rule : $\backslash nabla\_u(ap)=u(a)p+a\backslash nabla\_u(p),\; \backslash quad\; a\backslash in\; A,\; \backslash quad\; p\backslash in$ P. Connections on a module over a commutative ring always exist. The curvature of the connection $\backslash nabla$ is defined as the zero-order differential operator : $R(u,u\text{'})=()-\backslash nabla\_\; \backslash ,$ on the module $P$ for all $u,u\text{'}\backslash in\; D(A)$. If $E\backslash to\; X$ is a vector bundle, there is one-to-one correspondence between linear connections $\backslash Gamma$ on $E\backslash to\; X$ and the connections $\backslash nabla$ on the $C^\backslash infty(X)$-module of sections of $E\backslash to$ X. Strictly speaking, $\backslash nabla$ corresponds to the covariant differential of a connection on $E\backslash to\; X$. 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「Connection (algebraic framework)」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.