Nonseparable UHF algebras II: Classification

Abstract

For every uncountable cardinal $\kappa$ there are $2^\kappa$ nonisomorphic simple AF algebras of density character $\kappa$ and $2^\kappa$ nonisomorphic hyperfinite II$_1$ factors of density character $\kappa$. These estimates are maximal possible. All C*-algebras that we construct have the same Elliott invariant and Cuntz semigroup as the CAR algebra.