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arXiv · 1408.4033

A note on non-unital absorbing extensions

James Gabe
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Abstract

Elliott and Kucerovsky stated that a non-unital extension of separable $C^\ast$-algebras with a stable ideal, is nuclearly absorbing if and only if the extension is purely large. However, their proof was flawed. We give a counter example to their theorem as stated, but establish an equivalent formulation of nuclear absorption under a very mild additional assumption to being purely large. In particular, if the quotient algebra is non-unital, then we show that the original theorem applies. We also examine how this effects results in classification theory.

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James Gabe. 2014-08-18. A note on non-unital absorbing extensions. https://doi.org/10.2140/pjm.2016.284.383

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