Nonseparable CCR algebras

TL;DR

This paper constructs a vast family of nonseparable approximately matricial C*-algebras with identical K-theory to UHF algebras, extending the understanding of their classification and structure.

Contribution

It demonstrates the existence of many nonisomorphic CCR algebras sharing the same K_0 group as a given UHF algebra, generalizing noncommutative tori to nonseparable cases.

Findings

Existence of 2^κ nonisomorphic CCR algebras for each uncountable κ

All constructed algebras share the same K_0 group as the original UHF algebra

These algebras generalize noncommutative tori to nonseparable settings

Abstract

Extending a result of the first author and Katsura, we prove that for every UHF algebra $A$ of infinite type, in every uncountable cardinality $\kappa$ there are $2^\kappa$ nonisomorphic approximately matricial C*-algebras with the same $K_0$ group as $A$. These algebras are group \cstar-algebras `twisted' by prescribed canonical commutation relations (CCR), and they can also be considered as nonseparable generalizations of noncommutative tori.