Timeline for "Surprising" categorical equivalences
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
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| Mar 12, 2011 at 0:29 | comment | added | Peter Arndt | Sorry about the vage statements - I don't remember the exact state of affairs and am too busy to look it up right now. I think the C^*-book by Rordam, Larsen, Laustsen should give all details. | |
| Mar 12, 2011 at 0:27 | comment | added | Peter Arndt | I think the functor back is given by expressing a given OAG as limit of groups of the form Z^n with strong unit (k_1,...,k_n), which seems to be always possible. An OAG of this latter form is K_0 of the direct sum of matrix-rings M_{k_1}(C)+...+M_{k_n}(C). Then you take the limit over these C^*-algebras. On morphisms Elliott's theorem tells you that any OAG-morphism is K_0 of a C^*-morphism. The AF-algebras in this statement are not supposed to be separable, but I am not sure about unitality. | |
| Mar 7, 2011 at 0:06 | comment | added | Yemon Choi | What's the functor going from the category of OAGs with strong unit to the category of AF C*-algebras? (I assume that the morphisms in the latter category are the *-homomorphisms.) | |
| Mar 6, 2011 at 14:07 | history | edited | Peter Arndt | CC BY-SA 2.5 |
wrote more
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| Mar 6, 2011 at 14:00 | history | answered | Peter Arndt | CC BY-SA 2.5 |