Classification of C*-algebras: functors versus Borel cardinality (I)

Andrew Toms (Purdue University)

Saturday 13th November, 2010 10:00-11:00 326


What does it mean to classify a category of objects? This talk will explore two approaches through the lens of C*-algebra theory: complete invariants and Borel complexity. On the invariant side, we will trace the history of the classification of C*-algebras by K-theory, starting with the seminal work of Glimm and arriving at George Elliott’s classification functor formalism. On the other hand, we will discuss the idea of Borel reducibility, machinery from the world of descriptive set theory meant to quantify how difficult it is to assign invariants to isomorphism classes of a category in a computable way. Finally, we’ll see examples of interaction between these two approaches, where a classification by invariants leads to new results on the Borel complexity of nuclear separable C*-algebras.

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