Quasi-invariant lifts of completely positive maps for groupoid actions
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910005650784256 |
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| author | Bhattacharjee, Suvrajit Forough, Marzieh |
| author_facet | Bhattacharjee, Suvrajit Forough, Marzieh |
| contents | Let $G$ be a locally compact, Hausdorff, second countable groupoid and $A$ be a separable, $C_0(G^{(0)})$-nuclear, $G$-$C^*$-algebra. We prove the existence of quasi-invariant, completely positive and contractive lifts for equivariant, completely positive and contractive maps from $A$ into a separable, quotient $C^*$-algebra. Along the way, we construct the Busby invariant for $G$-actions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_07859 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quasi-invariant lifts of completely positive maps for groupoid actions Bhattacharjee, Suvrajit Forough, Marzieh Operator Algebras Let $G$ be a locally compact, Hausdorff, second countable groupoid and $A$ be a separable, $C_0(G^{(0)})$-nuclear, $G$-$C^*$-algebra. We prove the existence of quasi-invariant, completely positive and contractive lifts for equivariant, completely positive and contractive maps from $A$ into a separable, quotient $C^*$-algebra. Along the way, we construct the Busby invariant for $G$-actions. |
| title | Quasi-invariant lifts of completely positive maps for groupoid actions |
| topic | Operator Algebras |
| url | https://arxiv.org/abs/2405.07859 |