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Extensions of the UHF-algebra of 2∞-type by C⁎-algebras with continuous scale
Journal of Mathematical Analysis and Applications ( IF 1.2 ) Pub Date : 2021-01-14 , DOI: 10.1016/j.jmaa.2021.124959 Cangyuan Wang
中文翻译:
2的UHF-代数的扩展∞通过型Ç ⁎ -代数与连续刻度
更新日期:2021-01-20
Journal of Mathematical Analysis and Applications ( IF 1.2 ) Pub Date : 2021-01-14 , DOI: 10.1016/j.jmaa.2021.124959 Cangyuan Wang
Let A be the UHF-algebra of -type, B be a non-unital but σ-unital stably finite simple -algebra with real rank zero and a continuous scale. In this paper, we give a classification of the following essential extensions of A by : up to unitary equivalence. Denote by , the abelian group of unitary equivalence classes of essential extensions of A by . There is a group isomorphism defined by , where is the corona algebra of .
中文翻译:
2的UHF-代数的扩展∞通过型Ç ⁎ -代数与连续刻度
设A为的UHF代数类型,B是一个非单位但σ单位稳定有限的简单-实等级为零且具有连续标度的代数。在本文中,我们给出了下列基本扩展分类一个由:直至单一等价。表示为,是A by的基本扩展的unit等价类的阿贝尔群。有一个群体同构 被定义为 ,在哪里 是的电晕代数 。