翻訳と辞書 Words near each other ・ Clifford, Ontario ・ Clifford, Virginia ・ Clifford, West Yorkshire ・ Clifford, Wisconsin ・ Clifford-Constable baronets ・ Clifford-New Glasgow Historic District ・ Clifford-Warren House ・ Cliffords Mesne ・ Clifford McLaglen ・ Clifford McNulty ・ Clifford Menhennitt ・ Clifford Merrick ・ Clifford Meth ・ Clifford Milburn Holland ・ Clifford Miranda ・ Clifford module ・ Clifford module bundle ・ Clifford Mollison ・ Clifford Monks ・ Clifford Monohan ・ Clifford Morris ・ Clifford Mulenga ・ Clifford Nass ・ Clifford Nelson Fyle ・ Clifford Newby-Harris ・ Clifford Ngobeni ・ Clifford Nii Boi Tagoe ・ Clifford Odets ・ Clifford Ohiagu ・ Clifford Olson 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 Clifford module ： ウィキペディア英語版 Clifford module In mathematics, a Clifford module is a representation of a Clifford algebra. In general a Clifford algebra ''C'' is a central simple algebra over some field extension ''L'' of the field ''K'' over which the quadratic form ''Q'' defining ''C'' is defined. The abstract theory of Clifford modules was founded by a paper of M. F. Atiyah, R. Bott and Arnold S. Shapiro. A fundamental result on Clifford modules is that the Morita equivalence class of a Clifford algebra (the equivalence class of the category of Clifford modules over it) depends only on the signature . This is an algebraic form of Bott periodicity. ==Matrix representations of real Clifford algebras== We will need to study ''anticommuting'' matrices (''AB'' = −''BA'') because in Clifford algebras orthogonal vectors anticommute :$A\; \backslash cdot\; B\; =\; \backslash frac(\; AB\; +\; BA\; )\; =\; 0.$ For the real Clifford algebra $\backslash mathbb\_\backslash ,$, we need ''p'' + ''q'' mutually anticommuting matrices, of which ''p'' have +1 as square and ''q'' have −1 as square. :$\backslash begin$ \gamma_a^2 &=& +1 &\mbox &1 \le a \le p \\ \gamma_a^2 &=& -1 &\mbox &p+1 \le a \le p+q\\ \gamma_a \gamma_b &=& -\gamma_b \gamma_a &\mbox &a \ne b. \ \\ \end Such a basis of gamma matrices is not unique. One can always obtain another set of gamma matrices satisfying the same Clifford algebra by means of a similarity transformation. :$\backslash begin$ \gamma_ &=& S &\gamma_ &S^ \end where S is a non-singular matrix. The sets γ a' and γ a belong to the same equivalence class. 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「Clifford module」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.