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Remarks on the extension group for purely infinite corona algebras
Linear and Multilinear Algebra ( IF 0.9 ) Pub Date : 2020-08-16 P. W. Ng
中文翻译:
关于纯无限电晕代数的扩展群的说明
更新日期:2020-08-16
Linear and Multilinear Algebra ( IF 0.9 ) Pub Date : 2020-08-16 P. W. Ng
We study BDF theory in the context of (not necessarily simple) purely infinite corona algebras. Let be a nonunital separable simple C*-algebra with standard regularity properties for which is purely infinite (though not necessarily simple). Let be a separable nuclear C*-algebra. We prove a BDF Voiculescu decomposition theorem for maps from to , and use this to prove that is a group. Then, restricting to the case , for some compact metric space X, and has continuous scale, we provide characterizations of the neutral element for .
中文翻译:
关于纯无限电晕代数的扩展群的说明
我们在(不一定简单)纯无限电晕代数的背景下研究BDF理论。让 是具有标准正则性的非单位可分简单C *代数 是纯粹无限的(尽管不一定简单)。让是一个可分离的核C *代数。我们证明了BDF Voiculescu分解定理 至 ,并以此证明 是一个小组。然后,仅限于这种情况,对于某些紧凑的度量空间X,和 具有连续的尺度,我们提供中性元素的表征 。