Timeline for The groupoid $C^*$ algebra associated to a certain groupoid
Current License: CC BY-SA 4.0
22 events
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| May 6, 2018 at 14:55 | comment | added | მამუკა ჯიბლაძე | Yes, except not on $\mathbb N$ but on ${\mathbb N}^{\mathbb N}$. | |
| May 6, 2018 at 12:07 | comment | added | Ali Taghavi | @მამუკაჯიბლაძე Yes. Thank you. so your comment helped me to understand that the groupoid in the question is not a new structure, it is isomorphic to the groupoid associated to the equivalent relation on $\mathbb{N}$ collapsing all points to one point. Yes? and its resulting C* algebra is the inductive limit of Matrix algebras, yes? | |
| May 6, 2018 at 12:04 | history | edited | Ali Taghavi |
I remove three tags
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| May 6, 2018 at 5:31 | comment | added | მამუკა ჯიბლაძე | Oh I see thanks. Identity map is the embedding of the subset $G^0$ into $G^1$. So your groupoid is isomorphic to $G^0\times G^0$, with $r$ and $s$ the first and the second projection, and $G^0\hookrightarrow G^0\times G^0$ the diagonal, right? | |
| May 5, 2018 at 21:08 | comment | added | Ali Taghavi | @მამუკაჯიბლაძე Please see item 3 of definition 1 page 104. I think in the example of this post r and s play the role of left and right identity alainconnes.org/docs/book94bigpdf.pdf | |
| May 5, 2018 at 20:51 | comment | added | Ali Taghavi | @მამუკაჯიბლაძე The inclusion. But a groupoid has no a universal identity. I am following the definition of groupoid according to definition in the book of Alain Connes Non Commutative geometry. | |
| May 5, 2018 at 20:49 | comment | added | მამუკა ჯიბლაძე | If this is a groupoid it must have a map $i:G^0\to G^1$, assigning to an object of the groupoid its identity morphism. I asked what is this map in your case. | |
| May 5, 2018 at 20:47 | history | edited | Ali Taghavi | CC BY-SA 4.0 |
added 28 characters in body; edited tags
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| May 5, 2018 at 20:36 | history | edited | Ali Taghavi |
edited tags
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| May 5, 2018 at 20:30 | comment | added | Ali Taghavi | @მამუკაჯიბლაძე I still wonder what do you mean by identity. In this example, as usual, r is the right identity and s is the left identity. right? | |
| May 5, 2018 at 20:24 | comment | added | Ali Taghavi | @მამუკაჯიბლაძე I am not considering the (small) category definition but I am considering the other one. Am I missing some thing? | |
| May 5, 2018 at 20:21 | comment | added | Ali Taghavi | @მამუკაჯიბლაძე I guess that you mean "what is the inverse?" Yes? In this case the inverse of a sequence is given by swiching even and odd index, right? There are various definition of groupoid and I think we are following two different (but actually the same) definitions. | |
| May 5, 2018 at 20:13 | comment | added | მამუკა ჯიბლაძე | What are the identities? | |
| May 5, 2018 at 20:09 | history | edited | Ali Taghavi | CC BY-SA 4.0 |
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| May 5, 2018 at 20:02 | history | edited | Ali Taghavi | CC BY-SA 4.0 |
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| May 5, 2018 at 20:00 | history | undeleted | Ali Taghavi | ||
| May 5, 2018 at 19:49 | history | deleted | Ali Taghavi | via Vote | |
| May 5, 2018 at 19:49 | history | edited | Ali Taghavi | CC BY-SA 4.0 |
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| May 5, 2018 at 19:47 | history | undeleted | Ali Taghavi | ||
| May 5, 2018 at 19:46 | history | deleted | Ali Taghavi | via Vote | |
| May 5, 2018 at 19:44 | history | edited | Ali Taghavi | CC BY-SA 4.0 |
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| May 5, 2018 at 19:39 | history | asked | Ali Taghavi | CC BY-SA 4.0 |