Nonseparable CCR algebras

Abstract

Extending a result of the first author and Katsura, we prove that for every UHF algebra [Formula: see text] of infinite type, in every uncountable cardinality [Formula: see text] there are [Formula: see text] nonisomorphic approximately matricial C*-algebras with the same [Formula: see text] group as [Formula: see text]. These algebras are group C*-algebras “twisted” by prescribed canonical commutation relations (CCR), and they can also be considered as nonseparable generalizations of noncommutative tori.