Timeline for The socle of cokernel of irreducible monomorphisms in the AR quiver of type An/I is simple
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| May 24, 2016 at 5:43 | comment | added | milanelo | Thanks for all the explanations again! I will read the related articles to understand this problem. | |
| May 23, 2016 at 17:16 | comment | added | Julian Kuelshammer | @milanelo The cokernel of an irreducible monomorphism will always be a uniserial module, in particular will have simple socle. | |
| May 21, 2016 at 11:56 | comment | added | milanelo | In my language, here the arrows between the non-zero vertices of the representation of a cokernel is always linear, therefore it has a unique submodule S(i) with i the target of the representation. Can I understand it in this way for the case An/I ? | |
| May 21, 2016 at 11:43 | comment | added | milanelo | For the last sentence, why the end of a hook has a simple socle, or equivalently has a unique simple submodule? Thanks a lot for explanation! | |
| May 21, 2016 at 11:03 | comment | added | milanelo | Thank you for all the comments! What I mean precisely is all the irreducible morphisms between indecomposable modules in the AR quiver, i.e, all the arrows in the quiver. @Dag Oskar Madsen | |
| May 19, 2016 at 11:02 | comment | added | Dag Oskar Madsen | Perhaps when he writes "irreducible monomorphisms in the AR quiver" he is referring to (a subset of) the arrows in the AR quiver. | |
| May 19, 2016 at 10:59 | history | edited | Julian Kuelshammer | CC BY-SA 3.0 |
corrected, taking into account Dag Madsen's comment
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| May 19, 2016 at 10:54 | comment | added | Julian Kuelshammer | @DagOskarMadsen Thanks, I was implicitly assuming the OP meant this. | |
| May 19, 2016 at 10:06 | comment | added | Dag Oskar Madsen | You can sometimes append hooks to both ends of the string, can't you? Are you (and the OP) assuming that the target of the irreducible monomorphism is an indecomposable module? | |
| May 19, 2016 at 8:47 | history | answered | Julian Kuelshammer | CC BY-SA 3.0 |