Normal coactions extend to the C*-envelope
Abstract
We show that a normal coaction of a discrete group on an operator algebra extends to a normal coaction on the C*-envelope. This resolves an open problem attempted by several experts in the area, and provides a more direct proof of a prominent result of Sehnem. As an application, we resolve a question of X. Li, where we identify the C*-envelopes of the operator algebras of groupoid-embeddable categories and of cancellative right LCM monoids. This latter class includes many examples of monoids that are not group-embeddable.
Fields of Study & Subjects
Advanced Operator Algebra Research
Algebraic structures and combinatorial models
Homotopy and Cohomology in Algebraic Topology
Publication details
- Journal / source
- Advances in Mathematics
- Publisher
- Elsevier BV
- Volume
- 493
- Pages
- 110921–110921
- Publication date
- 24 March 2026
- Language
- EN