Timeline for Lengths and additive invariants which preserve positivity
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 29, 2023 at 20:57 | comment | added | Tim Campion | chasing down references in here: Decomposition and classification of length functions, Dario Spirito | |
| Nov 19, 2023 at 0:56 | comment | added | John Wiltshire-Gordon | @TimCampion Yes, I'm referring to the C^* algebra stuff. There's some characterization of all possible ordered abelian groups $K_0 A$ where $A$ is an AF-algebra. Since all these questions are trivial for semisimple categories, the AF case is a nice next example. | |
| Nov 17, 2023 at 23:33 | comment | added | Tim Campion | @LaurentMoret-Bailly Thanks! I'll have to dig into it -- it looks like whatever they're defining is somehow derived from the length function in some "base case". Very interesting! | |
| Nov 17, 2023 at 23:32 | comment | added | Tim Campion | @JohnWiltshire-Gordon Thanks, good points! What is Elliott's theorem? I'm searching and seeing some stuff on $C^\ast$-algebras, but I'm not sure that's what you're referring to. | |
| Nov 17, 2023 at 8:07 | comment | added | Laurent Moret-Bailly | For question 2, you can have a look at Lemma 5.3 of this preprint, where the group is the value group of a valuation ring. | |
| Nov 17, 2023 at 7:56 | comment | added | Laurent Moret-Bailly | Question 1: the objection raised by @JohnWiltshire-Gordon applies whenever $R$ is not local (and nonzero). On the other hand, if $R$ is local with residue field $k$, $Art(R)$ is generated by $k$, so the answer is yes. | |
| Nov 17, 2023 at 1:32 | comment | added | John Wiltshire-Gordon | For question 1, try $k \times k$ for a field k. For question 2 in a slightly different setting, there's Elliott's theorem. | |
| Nov 16, 2023 at 21:06 | history | asked | Tim Campion | CC BY-SA 4.0 |