Normal coactions extend to the C-envelope

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 considered by Kakariadis, Katsoulis, Laca, and X. Li, and provides an elementary proof of a prominent result of Sehnem. As an application, we resol...

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Bibliographic Details
Published in:arXiv.org 2024-03
Main Authors: Brix, Kevin Aguyar, Bruce, Chris, Dor-On, Adam
Format: Article
Language:English
Subjects:
Monoids
Online Access:Get full text
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Summary: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 considered by Kakariadis, Katsoulis, Laca, and X. Li, and provides an elementary proof of a prominent result of Sehnem. As an application, we resolve a question of Li by identifying the C*-envelope of the operator algebra arising from a groupoid-embeddable category and of cancellative right LCM monoids. This latter class includes many examples of monoids that are not group-embeddable.
ISSN:2331-8422