Timeline for ring structure of $KK_*(A,A)$ for a separable $C^*$-algebra $A$
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 18, 2017 at 11:45 | comment | added | Gabor Szabo | Oops -- I think I was confused about something there. Sorry about that. | |
| Apr 16, 2017 at 21:21 | comment | added | Rasmus | @GaborSzabo Ext doesn't vanish for finitely generated abelian groups, for instance $\mathrm{Ext}(\mathbb Z/2,\mathbb Z/2)\cong\mathbb Z/2$. | |
| Mar 8, 2017 at 6:56 | comment | added | Gabor Szabo | I think the UCT-answer in Paul's link is the canonical one here. Note that the Ext-part vanishes in many interesting cases, such as for instance when $K_*(A)$ is finitely generated, so all you are left with is the usual Hom-set of endomorphisms on $K_*(A)$. | |
| Mar 7, 2017 at 23:42 | comment | added | Sabrina Gemsa | @PaulSiegel thank you. Well, now that you mention it, I have never seen calculations of $KK(A,B)$ in non-trivial cases as well (I wasn't aware of it). I have seen some calculations using the universal coefficient theorem, but mostly in order to calculate the $K$-theory of $C^*$-algebras. (Thus, I guess that the answer of question 1. is "no" for non-trivial cases ) | |
| Mar 7, 2017 at 19:44 | comment | added | Paul Siegel | I asked an even less ambitious question several years ago, and the answers there might help with your question. mathoverflow.net/questions/51203/… | |
| Mar 7, 2017 at 16:29 | history | asked | Sabrina Gemsa | CC BY-SA 3.0 |