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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 G-spectrum ： ウィキペディア英語版 G-spectrum In algebraic topology, a G-spectrum is a spectrum with an action of a (finite) group. Let ''X'' be a spectrum with an action of a finite group ''G''. The important notion is that of the homotopy fixed point set $X^$. There is always :$X^G\; \backslash to\; X^,$ a map from the fixed point spectrum to a homotopy fixed point spectrum (because, by definition, $X^$ is the mapping spectrum $F(BG\_+,\; X)^G$.) Example: $\backslash mathbb/2$ acts on the complex ''K''-theory ''KU'' by taking the conjugate bundle of a complex vector bundle. Then $KU^\; =\; KO$, the real ''K''-theory. The cofiber of $X\_\; \backslash to\; X^$ is called the Tate spectrum of ''X''. == ''G''-Galois extension in the sense of Rognes == This notion is due to J. Rognes . Let ''A'' be an E∞-ring with an action of a finite group ''G'' and ''B'' = ''A''''hG'' its invariant subring. Then ''B'' → ''A'' (the map of ''B''-algebras in E∞-sense) is said to be a ''G-Galois extension'' if the natural map :$A\; \backslash otimes\_B\; A\; \backslash to\; \backslash prod\_\; A$ (which generalizes $x\; \backslash otimes\; y\; \backslash mapsto\; (g(x)\; y)$ in the classical setup) is an equivalence. The extension is faithful if the Bousfield classes of ''A'', ''B'' over ''B'' are equivalent. Example: ''KO'' → ''KU'' is a ℤ./2-Galois extension. 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「G-spectrum」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.