| 黎志华,薛以锋.纯无限单的C*-代数通过某些C*-代数扩张的非稳定K-理论[J].数学年刊A辑,2011,32(3):277~282 |
| 纯无限单的C*-代数通过某些C*-代数扩张的非稳定K-理论 |
| Nonstable K-theory for Extension Algebras of the Simple Purely Infinite C*-algebra by Certain C*-algebras |
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| DOI： |
| 中文关键词: K-群 纯无限单C~*-代数 实秩零 |
| 英文关键词:K-groups Simple purely infinite C~*-algebra Real rank zero |
| 基金项目:国家自然科学基金(No.10771069); 上海市重点学科建设基金(No.B407)资助的项目 |
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| 中文摘要: |
| 设$0 \rightarrow \B \stackrel{j}{\rightarrow} E \stackrel{\pi}{\rightarrow} \A \rightarrow 0$是有单位元$C^*$-代数$E$的一个扩张,
其中$\A$是有单位元纯无限单的$C^{*}$-代数, $\B$是$E$的闭理想. 当$\B$是$E$的本性理想并且同时是单的、可分的而且具有实秩零及性质(PC)时,
证明了$K_{0}(E)=\{[p] \mid p$是$E \setminus \B$中的投影\!\}; 当$\B$是稳定$C^{*}$-代数时, 证明了对任意紧的Hausdorff空间$X$,
有$\U(C(X,E))/\U_{0}(C(X,E)) \cong K_{1}(C(X,E))$. |
| 英文摘要: |
| Let $0 \rightarrow \B \stackrel{j}{\rightarrow} E \stackrel{\pi}{\rightarrow} \A \rightarrow 0$ be a
short exact sequence of the unital $C^{*}$-algebras,
where $\A$ is a unital simple purely infinite $C^{*}$-algebra, $\B$ is a closed ideal of the unital $C^{*}$-algebra $E$.
If $\B$ is an essential
ideal of $E$ and $\B$ is also simple, separable with $\RR(\B)=0$ and (PC), then $K_{0}(E)=\{[p] \mid p$ is a projection in
$E \setminus \B\}$; if $B$ is a stable $C^{*}$-algebra, then $\U(C(X,E))/\U_{0}(C(X,E)) \cong K_{1}(C(X,E))$
for any compact Hausdorff space $X$. |
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