Nonisomorphic simple AH~algebras with the same Elliott invariant and radius of comparison

N.Christopher Phillips  (University of Oregon)

9:30-10:30£¬ July 30th£¬2024    Tian Jiabing Building 323


For each $r > 0$, we exhibit an uncountable family of pairwise nonisomorphic AH algebras with the same Elliott invariant and with radius of comparison equal to~$r$. Our examples are "two seed Villadsen algebras". They are distinguished by a local radius of comparison function, naturally defined on the positive cone of the $K_0$~group. For each fixed~$r$, our examples are parametrized by an open interval, using the value of this function on a particular $K_0$~class. This result is a complement to the recent result of Elliott, Li, and Niu, which classifies certain Villadsen algebras of the first kind in terms of the Elliott invariant and radius of comparison. This is joint work with Ilan Hirshberg.

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