English

Essential Cartan subalgebras of $C^*$-algebras

Operator Algebras 2025-10-24 v5

Abstract

We define essential commutative Cartan pairs of CC^*-algebras generalising the definition of Renault and show that such pairs are given by essential twisted groupoid CC^*-algebras as defined by Kwa\'sniewski and Meyer. We show that the underlying twisted groupoid is effective, and is unique up to isomorphism among twists over effective groupoids giving rise to the essential commutative Cartan pair. We also show that for twists over effective groupoids giving rise to such pairs, the automorphism group of the twist is isomorphic to the automorphism group of the induced essential Cartan pair via explicit constructions.

Keywords

Cite

@article{arxiv.2206.09634,
  title  = {Essential Cartan subalgebras of $C^*$-algebras},
  author = {Jonathan Taylor},
  journal= {arXiv preprint arXiv:2206.09634},
  year   = {2025}
}

Comments

33 pages, version accepted for publication in Mathematica Scandinavica