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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 Graded manifold ： ウィキペディア英語版 Graded manifold In algebraic geometry, Graded manifolds are extensions of the manifold concept based on ideas coming from supersymmetry and supercommutative algebra. Both graded manifolds and supermanifolds are phrased in terms of sheaves of graded commutative algebras. However, graded manifolds are characterized by sheaves on smooth manifolds, while supermanifolds are constructed by gluing of sheaves of supervector spaces. ==Graded manifolds== A graded manifold of dimension $(n,m)$ is defined as a locally ringed space $(Z,A)$ where $Z$ is an $n$-dimensional smooth manifold and $A$ is a $C^\backslash infty\_Z$-sheaf of Grassmann algebras of rank $m$ where $C^\backslash infty\_Z$ is the sheaf of smooth real functions on $Z$. A sheaf $A$ is called the structure sheaf of a graded manifold $(Z,A)$, and a manifold $Z$ is said to be the body of $(Z,A)$. Sections of the sheaf $A$ are called graded functions on a graded manifold $(Z,A)$. They make up a graded commutative $C^\backslash infty(Z)$-ring $A(Z)$ called the structure ring of $(Z,A)$. The well-known Batchelor theorem and Serre-Swan theorem characterize graded manifolds as follows. 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「Graded manifold」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.