Nonstable $K$--theory for extension algebras of the simple purely infinite $C^*$--algebra by certain $C^{*}$--algebras
| Autor: | Li, Zhihua, Xue, Yifeng |
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| Rok vydání: | 2010 |
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| Druh dokumentu: | Working Paper |
| Popis: | Let $0\longrightarrow \B\stackrel{j}{\longrightarrow}E\stackrel{\pi}{\longrightarrow}\A\longrightarrow 0$ be an extension of $\A$ by $\B$, where $\A$ is a unital simple purely infinite $C^{*}$--algebra. When $\B$ is a simple separable essential ideal of the unital $C^{*}$--algebra $E$ with $\RR(\B)=0$ and {\rm(PC)}, $K_{0}(E)=\{[p]\mid p$ is a projection in $E\setminus B\}$; When $B$ is a stable $C^{*}$--algebra, $\U(C(X,E))/\U_0(C(X,E))\cong K_1(C(X,E))$ for any compact Hausdorff space $X$. Comment: 7 pages, Chinese Math. Annal (Chinese) (accepted) |
| Databáze: | arXiv |
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