A C * -diagonal in the Jiang–Su algebra via entangled matrix cones

We construct the Jiang–Su algebra [Formula: see text] as an inductive limit of dimension drop algebras, describing the latter as entangled matrix cones to explicitly define the connecting [Formula: see text]-homomorphisms. This construction gives rise to a [Formula: see text]-diagonal in [Formula: see text] with one-dimensional spectrum which is not locally connected. Along the way, we give a new characterisation of normalisers in Cartan pairs in terms of state excision.