The stunning result of Gong, Lin, and Niu (and its sequels)

Classification of operator algebras: complexity, rigidity, and dynamics

29 March 14:00 - 15:00

George Elliott - University of Toronto

For the first time, a little over a year ago, Guihua Gong, Huaxin Lin, and Zhuang Niu classified an axiomatically determined class of C*-algebras that exhausted the invariant for finite, unital, simple, separable C*-algebras with finite nuclear dimension. Later work, by a number of people, has distilled the axioms so that, in fact, this whole class itself is exhausted, with the possibly redundant addition of the UCT (Universal Coefficient Theorem). Even the property of finiteness can be dropped, if one incorporates the earlier (equally stunning) theorem of Kirchberg and Phillips in the infinite case. The (Toms-Winter) problem still remains of showing that finite nuclear dimension can be weakened to Jiang-Su stability, still assuming of course nuclearity. This has been shown (again by the work of a number of people---most of them in a single group!) in the interesting if special case that the traces constitute a Bauer simplex. (Examples of this are not hard to point to.)
Marius Dadarlat
Purdue University
Søren Eilers
University of Copenhagen
Asger Törnquist
University of Copenhagen


Søren Eilers


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