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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 Direct limit of groups ： ウィキペディア英語版 Direct limit of groups In mathematics, a direct limit of groups is the direct limit of a ''direct system'' of groups. These are central objects of study in algebraic topology, especially stable homotopy theory and homological algebra. They are sometimes called stable groups, though this term normally means something quite different in model theory. Certain examples of stable groups are easier to study than "unstable" groups, the groups occurring in the limit. This is ''a priori'' surprising, given that they are generally infinite-dimensional, constructed as limits of groups with finite-dimensional representations.; ==Examples== Each family of classical groups forms a direct system, via inclusion of matrices in the upper left corner, such as $\backslash operatorname(n,A)\; \backslash to\; \backslash operatorname(n+1,A)$. The stable groups are denoted $\backslash operatorname(A)$ or $\backslash operatorname(\backslash infty,A)$. Bott periodicity computes the homotopy of the stable unitary group and stable orthogonal group. The Whitehead group of a ring (the first K-group) can be defined in terms of $\backslash operatorname(A)$. Stable homotopy groups of spheres are the stable groups associated with the suspension functor. 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「Direct limit of groups」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.