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Normal coactions extend to the C*-envelope

Lookup NU author(s): Dr Chris BruceORCiD

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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.

Publication metadata

Author(s): Brix KA, Bruce C, Dor-On A

Publication type: Article

Publication status: Published

Journal: Advances in Mathematics

Year: 2026

Volume: 493

Print publication date: 01/05/2026

Online publication date: 24/03/2026

Acceptance date: 17/03/2026

Date deposited: 17/03/2026

ISSN (print): 0001-8708

ISSN (electronic): 1090-2082

Publisher: Elsevier

URL: https://doi.org/10.1016/j.aim.2026.110921

DOI: 10.1016/j.aim.2026.110921

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