Nonseparable UHF algebras II: Classification

Abstract

For every uncountable cardinal κ there are 2κ nonisomorphic simple AF algebras of density character κ and 2κnonisomorphic hyperfinite II1 factors of density character κ. These estimates are maximal possible. All C∗-algebras that we construct have the same Elliott invariant and Cuntz semigroup as the CAR algebra.