Nonseparable Uhf Algebras Ii: Classification

Ilijas Farah, Takeshi Katsura
2015 Mathematica Scandinavica  
For every uncountable cardinal $\kappa$ there are $2^\kappa$ nonisomorphic simple AF algebras of density character $\kappa$ and $2^\kappa$ nonisomorphic hyperfinite ${\rm II}_1$ 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.
doi:10.7146/math.scand.a-22238 fatcat:2wz3f6enbvfqdockwqtp74o5em