Timeline for Kac's theorem for quiver representations over an arbitrary ground field
Current License: CC BY-SA 3.0
4 events
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| Feb 27, 2018 at 19:59 | history | edited | Hugh Thomas | CC BY-SA 3.0 |
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| Feb 27, 2018 at 16:51 | comment | added | Julian Kuelshammer | Do you want to reduce to infinite fields (or what level of generality)? For finite fields, the number is of course finite for trivial reasons. In that case, another result by Kac shows that the number is given by a polynomial in $q$, the cardinality of the ground field. | |
| Feb 27, 2018 at 16:29 | comment | added | Julian Kuelshammer | This is probably not the case you are interested in, but for $Q$ of (extended) Dynkin type, the result should follow from the explicit classification of modules, see e.g. [Dlab, Ringel: Indecomposable representations of graphs and algebras] or [Ringel: Tame algebras and integral quadratic forms, Section 3.6]. | |
| Feb 27, 2018 at 15:36 | history | asked | Hugh Thomas | CC BY-SA 3.0 |