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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 Graph C*-algebra ： ウィキペディア英語版 Graph C*-algebra In mathematics, particularly the theory of C *-algebras, a graph C *-algebra is a universal C *-algebra associated to a directed graph. They form a rich class of C *-algebras encompassing Cuntz algebras, Cuntz-Krieger algebras, the Toeplitz algebra, etc. Also every AF-algebra is Morita equivalent〔D. Drinen,''Viewing AF-algebras as graph algebras'', Proc. Amer. Math. Soc., 128 (2000), pp. 1991–2000.〕 to a graph C *-algebra. As the structure of graph C *-algebras is fairly tractable with computable invariants, they play an important part in the classification theory of C *-algebras. ==Definition== Let $E=(E^0,\; E^1,\; r,\; s)$ be a directed graph with a countable set of vertices $E^0$, a countable set of edges $E^1$, and maps $r,\; s\; :\; E^1\; \backslash rightarrow\; E^0$ identifying the range and source of each edge, respectively. The graph C *-algebra corresponding to $E$, denoted by $C^$ *(E), is the universal C *-algebra generated by mutually orthogonal projections $\backslash$ and partial isometries $\backslash$ with mutually orthogonal ranges such that : (i) $s\_e^$ *s_e = p_ for all $e\; \backslash in\; E^1$ (ii) $p\_v\; =\; \backslash sum\_\; s\_e\; s\_e^$ * whenever (iii) $s\_e\; s\_e^$ * \le p_ for all $e\; \backslash in\; E^1$. 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「Graph C*-algebra」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.