Timeline for Homomorphism to multiplier algebra of groupoid $C^\ast$-algebra
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| Apr 12, 2018 at 12:24 | answer | added | Simon Henry | timeline score: 2 | |
| Apr 12, 2018 at 11:35 | comment | added | David Roberts♦ | @Simon yes, I only care in the case that X_0 is a disjoint summand of Y_0 (so a special case of taking a topological cofibration), but I think I can reduce to the case that the functor is the identity on objects. | |
| Apr 12, 2018 at 8:21 | comment | added | Simon Henry | Don't you also need $X_0$ to be open in $Y_0$ ? Other wise I don't see how you hope to get that for "discrete" groupoids (I mean discrete in the sense of $G_1=G_0$). | |
| Apr 12, 2018 at 8:16 | comment | added | Simon Henry | The reason Lemma 7 of the reference you quote does not use multiplier is because they only construct that morphism in the case of a cofibrations of groupoid, which are injective on objects. | |
| Apr 12, 2018 at 6:05 | history | edited | David Roberts♦ | CC BY-SA 3.0 |
added 234 characters in body
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| Apr 11, 2018 at 14:46 | comment | added | Mateusz Wasilewski | I am sorry, you are right; I too hastily assumed that the situation in this respect is the same as for groups. | |
| Apr 11, 2018 at 1:35 | comment | added | David Roberts♦ | ...or even just not finite? | |
| Apr 10, 2018 at 22:14 | comment | added | David Roberts♦ | @MateuszWasilewski hang on, what if the set of units of the groupoid is uncountable? | |
| Apr 10, 2018 at 12:23 | comment | added | Mateusz Wasilewski | In the discrete case the algebras are unital, so the multiplier algebra does not enter the picture. | |
| Apr 10, 2018 at 5:51 | comment | added | David Roberts♦ | While I'm not confident in the addendum any more, the comments before Lemma 7 in Localization of Cofibration Categories and Groupoid $C^\ast$-algebras (arxiv.org/pdf/1609.03805.pdf) claim something similar for discrete groupoids (though without mentioning the multiplier algebra, so I'm a bit wary). | |
| Apr 7, 2018 at 3:19 | history | asked | David Roberts♦ | CC BY-SA 3.0 |