Dan Kucervosky - An abstract Brown-Douglas-Fillmore absorption theorem, I

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Dan Kucervosky - An abstract Brown-Douglas-Fillmore absorption theorem, I

DAN KUCERVOSKY, Fields Institute, Toronto, Ontario, Canada

An abstract Brown-Douglas-Fillmore absorption theorem, I

A common generalization is given of all previous absorption theorems for $C^\ast$ -algebra extensions. We consider extensions of a stable, nuclear, separable $C^\ast$ -algebra by an arbitrary separable $C^\ast$ -algebra, and in this setting, we give a simple intrinsic criterion for an extension to be absorbing. The criterion involves only the $C^\ast$ -algebra of the extension, together with the canonical closed two-sided ideal. This is joint work with George Elliott.