Non-isomorphic simple AH algebras with the same Elliott invariant and same radius of comparison

Ilan Hirshberg (Ben-Gurion University)

Thursday 23rd May 16:00-17:00 Maths 116


Recently, Elliott, Li and Niu proved a classification theorem for Villadsen-type algebras using the combination of the Elliott invariant and the radius of comparison, an invariant which was introduced by Toms in order to distinguish between certain non-isomorphic AH algebras with the same Elliott invariant. This might have raised the prospect that the Elliott classification program can be extended beyond the Z-stable case by adding the radius of comparison to the invariant. I will discuss a recent preprint in which we show that this is not the case: we construct an uncountable family of non-isomorphic AH algebras with the same Elliott and same radius of comparison. We can distinguish between them using a finer invariant, which we call the local radius of comparison.

This is joint work with N. Christopher Phillips.

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