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Nonseparable Uhf Algebras Ii: Classification

Ilijas Farah, Takeshi Katsura


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.

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ISSN 0025-5521 (print) ISSN 1903-1807 (online)

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