The Fields Institute Turns Twenty-Five 170725 Final book with covers | Page 166

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George Elliott
participants, Eberhard Kirchberg and Chris Phillips, who
made an enormous impact on the C*-algebra classification
theory that I had proposed a few years before. Their
completely abstract, axiomatic result towered over earlier
results obtained in more concrete settings, completely settling
the (well-behaved) infinite case. The finite case is only now
being worked out, with unital simple (well-behaved) algebras
now covered by a uniform axiomatic framework in both the
finite and infinite cases. (The non-unital simple case is
recalcitrant, but close to completion, and the non-simple case
has advanced quite far, although it does not follow from the
simple case as it did over thirty years ago for von Neumann
algebras, in the work of Connes, Haagerup, Krieger, and
Takesaki.)
George Elliott, Juris Steprans, and Bradd Hart at a reception
at the Fields Institute, 2005.