| 刘树冬,方小春.纯无限单C*-代数的扩张代数的K-理论Ⅱ[J].数学年刊A辑,2009,30(3):433~438 |
| 纯无限单C*-代数的扩张代数的K-理论Ⅱ |
| K-Theory for Extensions of Purely Infinite Simple C*-algebras Ⅱ |
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| DOI： |
| 中文关键词: C*-代数 扩张 K*理论 纯无限 |
| 英文关键词: |
| 基金项目:国家自然科学基金，山东省自然科学基金(No.Y2006A03)资助的项目 |
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| 中文摘要: |
| 给出了有单位元的纯无限单的C*-代数A通过K的扩张代数E的K-理论的一种刻画.证明了K0(E)同构于E中所有具有无限余投影的无限投影的Murry-yon Neumann等价类全体所成的交换群,它还同构于上述投影的同伦等价类或酉等价类全体所成的交换群.还证明了对扩张代数E中的任·满的正元a,存在元索z ∈E,使得x*ax=1,其中K为可分无限维Hilbert空间上紧算子全体所成的C*一代数. |
| 英文摘要: |
| This paper describes $K$-theory for C*-algebra $E$ which is the extension of a
purely infinite simple C*-algebras $A$ by ${\k}$, the C*-algebra of all compact oprators on separable \linebreak
infinite
dimensional Hilbert space.
It is proved that $K_0(E)$ is the group of all Murry-von Neumann equivalent classes of all
infinite projections in $E$ with infinite complement projections,
it is also equal to the group of all homotopy
equivalent classes or unitary equivalent classes of the above projections.
The authors also prove that for any full positive
element $a\in E$, there exists an element $x\in E$, such that $x^*ax=1.$ |
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