Timeline for Quivers for algebras which are not basic or unital.
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 14, 2013 at 4:07 | comment | added | Kevin Walker | @Dag: Yes, that does look like what I had in mind -- thanks! | |
| Apr 13, 2013 at 21:31 | comment | added | Dag Oskar Madsen | @Kevin: I haven't looked at it very closely, but I think they are doing something like that in section 3 of arXiv:1303.7049 | |
| Apr 13, 2013 at 16:39 | comment | added | Kevin Walker | My guess is that in the non-basic case one could start with the quiver for a Morita-equivalent basic algebra (as described above by B. Steinberg), then interpret each vertex $v_i$ as representing a $k_i \times k_i$ matrix algebra, each edge as representing a rectangular $k_i \times k_j$ matrix of elements of the radical, and so on. I don't know of a reference for this construction, and I would be very interested to know if there is one. | |
| Apr 13, 2013 at 14:44 | comment | added | Benjamin Steinberg | For unital non-basic algebras there is a unique up to isomorphism unital basic algebra which is Morita equivalent to it and one uses that algebras quivers. I don't have a good answer for the nonunital case unless you want to add a unit. | |
| Apr 13, 2013 at 13:29 | history | asked | Jianrong Li | CC BY-SA 3.0 |