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

Lukas Obermeyer; Wilhelm Winter

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

Operator Algebras 2026-07-03 v1

Authors: Lukas Obermeyer , Wilhelm Winter

Abstract

We construct the Jiang-Su algebra Z as an inductive limit of dimension drop algebras, describing the latter as entangled matrix cones to explicitly define the connecting *-homomorphisms. This construction gives rise to a C*-diagonal in Z 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.

Keywords

Jiang-Su algebra C*-diagonal Cartan pair dimension drop algebra inductive limit normaliser

Cite

@article{arxiv.2607.03129,
  title  = {A C*-diagonal in the Jiang-Su algebra via entangled matrix cones},
  author = {Lukas Obermeyer and Wilhelm Winter},
  journal= {arXiv preprint arXiv:2607.03129},
  year   = {2026}
}

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34 pages