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

__Abstract:__

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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