Timeline for K-Theory of $C^{*}(X)$
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 30, 2020 at 20:28 | vote | accept | Peg Leg Jonathan | ||
| Aug 29, 2020 at 20:19 | comment | added | Peg Leg Jonathan | I appreciate it, sir. | |
| Aug 29, 2020 at 19:11 | comment | added | Ulrich Pennig | Karen Strung has good notes about C*-algebras in the context of the classification programme. They also treat K-theory and can be found here: strung.me/karen/CStarIntroDraft.pdf . Maybe these are useful. | |
| Aug 29, 2020 at 18:54 | comment | added | Peg Leg Jonathan | @UlrichPennig Thank you very much sir. I learned a lot from your answer. It is clear now for me. | |
| Aug 29, 2020 at 18:49 | comment | added | Ulrich Pennig | As for the group $C^*$-algebra, I guess the answer is: It is what it is. You can view it as the direct limit over all $C^*$-algebras $C^*(S_n)$, which reveals it as an AF-algebra, if that helps. The algebras $C^*(S_n)$ are of course finite-dimensional and can be seen as direct sums of matrix algebras. | |
| Aug 29, 2020 at 18:47 | comment | added | Ulrich Pennig | You wrote you consider the group of finite support bijections of $\mathbb{N}$. Such a bijection is the identity outside of a finite set and permutes the elements in that finite set. Therefore you can identify the group of finite support bijections with the union over all groups $S_n$. Does that help? | |
| Aug 29, 2020 at 18:04 | comment | added | Nik Weaver | @PegLegScott please don't take this the wrong way, but it really doesn't look like you have enough background to be studying K-theory of C*-algebras. Why not start a little further back? | |
| Aug 29, 2020 at 16:46 | comment | added | Peg Leg Jonathan | Thank you for your answer sir, but I don't understand the first paragraph: The group is infinite symmetric group, how do you know that? And second what is its $C^{*}$-algebra? Sorry if my questions are so dumb. | |
| Aug 29, 2020 at 16:14 | history | answered | Ulrich Pennig | CC BY-SA 4.0 |