Inductive limits of 1-dimensional NCCW complexes with trivial K1-groups and injective unital connecting maps always admit a C*-diagonal.
A classification of inductive limits of splitting interval algebras
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abstract
It is shown that the Cuntz semigroup is a complete invariant for the C*-algebras that can be realized as an inductive limit of a sequence of finite direct sums of splitting interval algebras.
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$C^*$-diagonal of inductive limit of $1$-dimensional NCCW complexes
Inductive limits of 1-dimensional NCCW complexes with trivial K1-groups and injective unital connecting maps always admit a C*-diagonal.