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.

References in corpus (2)

• Graphs and CCR algebras
• Omitting types and AF algebras