Approximate Unitary Equivalence of Homomorphisms from O ∞ *
Approximate Unitary Equivalence of Homomorphisms from O ∞ *
复制标题
O ∞ * 的同态近似酉等价
DOI：
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发表时间：
1994
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通讯作者：
N. Phillips
中科院分区：
文献类型：
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作者：
N. Phillips
证明了若从O∞到一个纯无限单C-代数的两个同态在KK-理论中有相同的类，且若两者都是酉的或都是非酉的，则它们近似酉等价.因此，O∞在Rørdam意义下是可分类的。特别地，Rørdam关于偶Cuntz代数上矩阵代数的直接极限的分类定理推广到偶Cuntz代数上的矩阵代数和O∞的角的直接极限，其中K 0-群可以是任意可数的没有偶挠的阿贝尔群。
We prove that if two homomorphisms from O∞ to a purely infinite simple C-algebra have the same class in KK-theory, and if either both are unital or both are nonunital, then they are approximately unitarily equivalent. It follows that O∞ is classifiable in the sense of Rørdam. In particular, Rørdam’s classification theorem for direct limits of matrix algebras over even Cuntz algebras extends to direct limits involving both matrix algebras over even Cuntz algebras and corners of O∞, for which the K0-group can be an arbitrary countable abelian group with no even torsion.