Non-traditional C*-diagonals in twisted groupoid C*-algebras

Anna Duwenig

Non-traditional C-diagonals in twisted groupoid C-algebras

Operator Algebras 2025-05-26 v1

Authors: Anna Duwenig

Abstract

We identify which conditions on an open normal subgroupoid of a LCH \'etale groupoid with twist are necessary and sufficient for the subgroupoid's reduced twisted C*-algebra to be a C*-diagonal in the ambient groupoid C*-algebra. We do so by first giving an explicit description of the Weyl groupoid and Weyl twist associated to any non-traditional Cartan subalgebra, that is, a Cartan subalgebra that is induced from a non-trivial open normal subgroupoid, as studied in [DWZ2025]. We then combine this description with Kumjian-Renault theory to establish the necessary and sufficient conditions to get a C*-diagonal.

Keywords

C*-algebra groupoid Cartan subalgebra Weyl groupoid twisted algebra

Cite

@article{arxiv.2505.17913,
  title  = {Non-traditional C*-diagonals in twisted groupoid C*-algebras},
  author = {Anna Duwenig},
  journal= {arXiv preprint arXiv:2505.17913},
  year   = {2025}
}

Comments

33 pages