Timeline for Certain groupoid and its $C^{*}$ algebra
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Oct 13, 2016 at 18:55 | vote | accept | Ali Taghavi | ||
| Oct 10, 2016 at 12:13 | answer | added | Simon Henry | timeline score: 1 | |
| Oct 10, 2016 at 9:52 | comment | added | Simon Henry | If I'm not mistaken, the groupoid you obtain is equivalent to the free group on $(n-2)(n-1)/2$ generators. So this algebra you obtain should be isomorphic (possibly non canonically) to something like the algebra of $n$ by $n$ matrix with coefficient in the algebra of the free group on $(n-2)(n-1)/2$ generators. | |
| Oct 10, 2016 at 9:36 | comment | added | Simon Henry | What do you cal the "groupoid associated with this semi-group" ? The localization at all arrows ? (i.e. the groupoid obtained by formally inverting all arrow) If so I really don't think the $C^*$-algebra you will obtain will be finite dimensional... Unless you have a reason to say it will be that I missed ? | |
| Oct 10, 2016 at 8:07 | history | edited | Ali Taghavi | CC BY-SA 3.0 |
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| Oct 9, 2016 at 20:34 | comment | added | Uri Bader | You will probably end up having $\text{Mor}(x,y)$ being the full free abelain group generated by $X$ for all $x,y$. | |
| Oct 9, 2016 at 20:23 | history | edited | Ali Taghavi | CC BY-SA 3.0 |
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| Oct 9, 2016 at 20:02 | history | edited | Ali Taghavi | CC BY-SA 3.0 |
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| Oct 9, 2016 at 19:51 | history | asked | Ali Taghavi | CC BY-SA 3.0 |