Timeline for Representation-finite symmetric monoid algebras
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| Jul 1, 2017 at 5:11 | answer | added | Benjamin Steinberg | timeline score: 2 | |
| Jun 30, 2017 at 16:35 | comment | added | Mare | Well, the classification of selfinjective or symmetric quiver algebras is known. So in principle yes. But of course Im aiming for a nice criterion such as for group algebras instead of some criterion using relations. Maybe replace cyclic Sylow group by "cyclic something else" and add some conditions? But I have no experience with monoid algebras expect from reading some chapters in your book. | |
| Jun 30, 2017 at 15:08 | comment | added | Benjamin Steinberg | Ok. In any event the algebra of any quiver with relations all of the form $a=0$ or $a-b=0$ is essentially a monoid algebra. Can you say when these are self injectives and Representation finite? | |
| Jun 30, 2017 at 14:03 | history | edited | Mare | CC BY-SA 3.0 |
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| Jun 30, 2017 at 13:57 | comment | added | Mare | @benjaminSteinberg The result is the same. Selfinjective forces indecomposable projectives to have simple socles. For monomial algebras, thats only possible if the monomial algebra is a nakayama algebra, meaning its quiver is a circle. | |
| Jun 30, 2017 at 12:00 | comment | added | Benjamin Steinberg | I should say symmetric not representation finite. | |
| Jun 30, 2017 at 11:56 | comment | added | Benjamin Steinberg | Is that easy to see from the relations? I know how to characterize these if the monoid is regular. | |
| Jun 29, 2017 at 13:50 | comment | added | Mare | Yes thats easy. A monomial algebra is symmetric iff it is a symmetric nakayama algebra. | |
| Jun 29, 2017 at 13:21 | comment | added | Benjamin Steinberg | This is too hard to do. It is equivalent to asking the same for all finite categories. Can you answer this for all monimial algebras | |
| Jun 29, 2017 at 8:19 | history | edited | Mare | CC BY-SA 3.0 |
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| Jun 29, 2017 at 8:14 | history | asked | Mare | CC BY-SA 3.0 |