Normal coactions extend to the C*-envelope
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866917381028184064 |
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| author | Brix, Kevin Aguyar Bruce, Chris Dor-On, Adam |
| author_facet | Brix, Kevin Aguyar Bruce, Chris Dor-On, Adam |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_04817 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Normal coactions extend to the C*-envelope Brix, Kevin Aguyar Bruce, Chris Dor-On, Adam Operator Algebras Primary: 46K50, 46L05, 47L55, Secondary: 46L55, 47L65 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. |
| title | Normal coactions extend to the C*-envelope |
| topic | Operator Algebras Primary: 46K50, 46L05, 47L55, Secondary: 46L55, 47L65 |
| url | https://arxiv.org/abs/2309.04817 |