Timeline for Recovering an abelian category from the Ext of its simple objects
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 7, 2021 at 6:38 | vote | accept | user49822 | ||
| May 2, 2021 at 6:14 | comment | added | Vladimir Dotsenko | @PedroTamaroff since the operad of associative algebras is non-symmetric, assumptions on the ground field are not necessary. Some finite-dimensionality conditions might be useful just to ensure that things do not explode. | |
| May 1, 2021 at 19:31 | comment | added | Jeremy Rickard | @PedroTamaroff Yes, if I remember correctly, if $B$ is a finite dimensional algebra, you can recover $\operatorname{mod}B$ from the $\operatorname{Ext}$-algebra of the direct sum of the simple $B$-modules with its natural $A_\infty$-structure. I don't think the characteristic of the field is relevant. | |
| May 1, 2021 at 15:48 | comment | added | Pedro | I presume one can try to use some higher structure in Ext to distinguish them (and even recover the derived categories?) in the cases you mentioned? As the other answer shows, at least in the last two examples, the culprit is indeed the existence of non trivial higher products. I know this works in char zero but I don't know what happens in the modular case. | |
| May 1, 2021 at 8:41 | history | answered | Jeremy Rickard | CC BY-SA 4.0 |