Timeline for Defining cluster algebras of finite type $\mathrm{A}$ by generators and relations
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 13, 2021 at 14:44 | comment | added | amator2357 | I see. Thank you, Jan. | |
| Jan 13, 2021 at 12:33 | comment | added | Jan Grabowski | (2,n) Grassmannians only provide a model of a type A cluster algebra with a particular choice of coefficients. The coordinate ring of its big Schubert cell is another, with different coefficients and different relations. It's not clear to me that using models in this way will give an answer to the question as asked. Nevertheless, I think that this should be true (being finite type A is very strong) but I don't know of a reference or how to prove it directly. | |
| Jan 13, 2021 at 9:55 | comment | added | amator2357 | Yes, when we don't invert the coefficients, this is true. I am still not sure if it holds if we do invert them (the coefficients). | |
| Jan 12, 2021 at 23:52 | comment | added | Sam Hopkins | Since these are coordinate rings of Grassmannians of the form $\mathrm{Gr}(2,n)$, for which the defining equations are the 3-term Plucker relations, this should be true. | |
| Jan 12, 2021 at 23:50 | history | asked | amator2357 | CC BY-SA 4.0 |