Timeline for Generalisation of the equivalence between $C^*(H)$ and $C_0(G/H) \rtimes G$; induction of group actions on C*-algebras
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 4, 2022 at 6:58 | vote | accept | Motmot | ||
| Aug 3, 2022 at 19:58 | answer | added | user85913 | timeline score: 3 | |
| Jul 28, 2022 at 13:08 | answer | added | Benjamin Steinberg | timeline score: 3 | |
| Jul 28, 2022 at 11:53 | comment | added | Benjamin Steinberg | I think you can use $X\times G$ as a bibundle | |
| Jul 28, 2022 at 11:45 | comment | added | Benjamin Steinberg | Actually I think it is not too bad to give a morita equivalence of the associated transformation groupoids which via Renault will give your Morita equivalence | |
| Jul 28, 2022 at 10:48 | comment | added | Benjamin Steinberg | So this should give the Morita equivalence you seek. | |
| Jul 28, 2022 at 10:47 | comment | added | Benjamin Steinberg | I think the answer to your first question is yes but I'm not a C*-algebraist.The action of $H$ on $X$ extends to a partial action of $G$ on $X$ in the sense of Exel by leaving the action of the other elements of $G$ undefined.I believe that $C(X)\rtimes H$ is the same as the partial action crossed product of $G$ with $C(X)$ coming from this partial action. The enveloping action or globalization of this partial action is $X\times_H G$.It's a result of Abadie that if the enveloping action is Hausdorff then there is Morita equivalence of the partial crossed product with the full crossed product. | |
| Jul 28, 2022 at 10:40 | history | edited | Matthew Daws | CC BY-SA 4.0 |
Fix Latex/Markdown issues
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| S Jul 28, 2022 at 8:10 | review | First questions | |||
| Jul 28, 2022 at 10:11 | |||||
| S Jul 28, 2022 at 8:10 | history | asked | Motmot | CC BY-SA 4.0 |