Timeline for Higher analogue of the Auslander-Bridger transpose
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 7, 2020 at 6:17 | comment | added | Oeyvind Solberg | If you apply the duality to $\operatorname{Tr}\Omega^{n-2}(M)$, then you get the $(n-1)$-Auslander-Reiten translation of $M$ (see sciencedirect.com/science/article/pii/S0001870806001721). | |
| May 6, 2020 at 15:50 | comment | added | Mare | @JeremyRickard Thanks, one can find that in their book. I would hope that somewhere in the literature there has appeared an official name for that and not just a symbol. (maybe in the theory of general noetherian rings, which I do not follow very closely) | |
| May 6, 2020 at 14:20 | comment | added | Jeremy Rickard | You probably already know that the cokernel of $P_{n-2}^{*} \rightarrow P_{n-1}^{*}$ is $\text{Tr }\Omega^{n-2}M$. I don't know a name, but Auslander and Bridger gave it a symbol, $J_{n-2}M$. | |
| May 6, 2020 at 11:49 | comment | added | Pedro | Ah! I see. Thanks! :) | |
| May 6, 2020 at 11:39 | comment | added | Mare | @PedroTamaroff I think Tr is called Auslander-Bridger transpose (which exists for any noetherian ring) while $\tau$=DTr is called Auslander-Reiten translate for Artin algebras. | |
| May 6, 2020 at 11:37 | comment | added | Pedro | Isn't your $\mathrm{Tr}(M)$ what people call the Auslander--Reiten transpose? Or am I missing something? (Perhaps just different nomenclature?) | |
| May 6, 2020 at 11:26 | history | edited | Mare | CC BY-SA 4.0 |
added 18 characters in body
|
| May 6, 2020 at 10:47 | history | asked | Mare | CC BY-SA 4.0 |