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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 Classifying space for U(n) ： ウィキペディア英語版 Classifying space for U(n) In mathematics, the classifying space for the unitary group U(''n'') is a space BU(''n'') together with a universal bundle EU(''n'') such that any hermitian bundle on a paracompact space ''X'' is the pull-back of EU(''n'') by a map ''X'' → BU(''n'') unique up to homotopy. This space with its universal fibration may be constructed as either # the Grassmannian of ''n''-planes in an infinite-dimensional complex Hilbert space; or, # the direct limit, with the induced topology, of Grassmannians of ''n'' planes. Both constructions are detailed here. ==Construction as an infinite Grassmannian== The total space EU(''n'') of the universal bundle is given by :$EU(n)=\backslash left\; \backslash \; \backslash right\; \backslash \}.$ Here, ''H'' is an infinite-dimensional complex Hilbert space, the ''e''''i'' are vectors in ''H'', and $\backslash delta\_$ is the Kronecker delta. The symbol $(\backslash cdot,\backslash cdot)$ is the inner product on ''H''. Thus, we have that EU(''n'') is the space of orthonormal ''n''-frames in ''H''. The group action of U(''n'') on this space is the natural one. The base space is then :$BU(n)=EU(n)/U(n)$ and is the set of Grassmannian ''n''-dimensional subspaces (or ''n''-planes) in ''H''. That is, :$BU(n)\; =\; \backslash$ so that ''V'' is an ''n''-dimensional vector space. 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「Classifying space for U(n)」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.